1. C h a p t e r 1 : F i n a n c i a l M a t h e m a t i c s ;
I n v e s t i n g M o n e y P i s $ 1 0 0 0 ; r i s 6 % o r 0 . 0 6 ; f is 5
4 = 1000(1 + ( 0 . 0 6 K 5 ) )
Note: Answers obtained in these exercises may vary A = 1300
I the technology used.
T h e f u t u r e v a l u e is $ 1 3 0 0 ,
I r-nson 1 1 S i m p l e I n t e r e s t , p a c j e 14 CA P ( 1 + rt)
"i.idOO; r i s 5 % o r 0 , 0 5 ; f is 5
.': - 0 0 0 ; r is 3 . 5 % o r 0 . 0 3 5 ; t is 8 ^000(1 + (0,05)(5))
)0(1 + (0.035K8)) 0
)0 n - ' - i ' j h i r e value . •* i • .Q
e v a l u e is $ 3 8 4 0 0 . I J /- /'(I +rt)
h i A- Pfi + rt)
r ' -00; r i s 5 % o r 0 , 0 5 ; f is 6
300; r i s 1.25% o r 0 , 0 1 2 5 ' f is 4 ••.'•'0(1 + ( 0 . 0 5 K 6 ) )
)0(1 + ( 0 . 0 1 2 5 K 4 ) ) ru)0
' •«"!>re v a l u e < . o r m a
3 v a l u e is $ 1 0 5 0 0 . ' n.h A yields the greatest future value,
c)A = P(1 + ff)
i e the interest earned
F is $ 2 5 0 0 0 ; r is 0 . 5 % or 0 . 0 0 5 ' t is 2
1 3 1 2 . 5 0 ^ 1 0 0 0 = 312,50
•0(1 + (0.005K2))
0 Rate of return = 3 1 2 ^
1000
i v a l u e is $ 2 5 2 5 0 .
Rate of r e t u m = 0,3125
T h e r a t e o f r e t u r n f o r o p t i o n A is 3 1 . 2 5 % .
• -iOO; r i s 7 . 4 % o r 0 , 0 7 4 ; f is 2 0
0(1 + (0.074)(20))
/ * 0 rt)
.-f v a l u e is $ 2 9 7 6 0 . $4000; r i s 2 . 3 % or 0.023; l i s 5
2.a)A = P+ Pn 1000(1 + ( 0 , 0 2 3 X 5 ) )
1460
'.'..11; P = $ 5 0 0 ( •
. 5 y e a r s , t h e f u t u r e v a l u e is $ 4 4 6 0
5000+(5000)(f)(5)
(',00 = 2 5 OOOf P is $ 4 0 0 0 ; f is 2 . 3 % o r 0 . 0 2 3 - f is 10
I :>.')•} A = 4000(1 +(0.023)(10))
A = 4920
0.06 = f A f t e r 10 y e a r s , t h e f u t u r e v a l u e is $ 4 9 2 0 ,
6500 - 5000 + (5000)(r)(5)
5.A = P ( 1 + rt)
1f/»(i 2*,000r
6 B r a d ' s G I C : P is $ 1 5 0 0 0 ; r i s 3 . 2 % o r 0 . 0 3 2 ' t is 6
/ I' Of 10(1 + ( 0 . 0 3 2 ) ( 6 ) )
Ar. i . i t - , f r , t rate o f 6 % will a l l o w C a m to r e a c h his g o a l ' ' ' ' 7 mm
I he r.itu.e v a l u e o f B r a d ' s i n v e s t m e n t is $ 1 7 8 8 0
P IS $ 5 0 0 0 : f is 6 % o r 0 . 0 6 ; t is 3 C i . r i - . G I C ; P is $ 1 5 0 0 0 ; r is 3 . 3 % o r 0 0 3 3 ' t is 5
71 = 5 0 0 0 ( 1 + ( 0 . 0 6 K 3 ) ) 15 0.30(1 + ( 0 , 0 3 3 ) ( 5 ) )
A = 5900 ^ ' 17 4 7 5
C a m will h a v e $ 5 9 0 0 .
f f i C f u t u r e v a l u e o f C h r i s ' s i n v e s t m e n t is $ 1 7 4 7 5
3. a) A = P ( 1 + rt)
B r a d ' s i n v e s t m e n t will h a v e a g r e a t e r f u t u r e v a l u e
P i s $1000; r i s 5 % o r 0 . 0 5 ; n s 5 at m a t u r i t y . I n v e s t i n g t h e m o n e y f o r o n e m o r e y e a r
.4 = 1 0 0 0 ( 1 + ( 0 , 0 5 ) ( 5 ) )
r e s u l t s in m o r e i n t e r e s t e a r n e d t h a n d o e s i n v e s t i n q
A = 1250
t h e m o n e y at a 0,1 % h i g h e r i n t e r e s t r a t e .
T h e f u t u r e v a l u e is $ 1 2 5 0 .
Determine the interest e a r n e d . G.a}A = P + Prt
1 2 5 0 ^ 1000 = 2 5 0
A $ 1 5 0 0 0 , F = $ 1 2 0 0 0 , f = 10
Rate of return = ^ 15 0 0 0 = 12 0 0 0 + ( l 2 0 0 0 ) ( r ) ( l 0 )
1000
3 0 0 0 = 120 OOOr
Rate of return = 0.25
^J3000_^
T h e r a t e o f r e t u r n is 2 5 %
b | A 71 - P ( 1 -rrl) 120 0 0 0
P i s $ 1 0 5 0 ; r i s 5 % o r 0 . 0 5 ; f is 5 0.025 = f
A = 1050(1 + (0.05)(5)) A n i n t e r e s t r a t e o f 2 . 5 % is n e e d e d f o r t h e C S B to
A = 1312.50 g r o w t o $ 1 5 0 0 0 in 10 y e a r s .
T h e f u t u r e v a l u e is $ 1 3 1 2 . 5 0 .
F o u n d a t i o n s o f M a t h e m a t i c s 12 S o l u t i o n s M a n u a l
1-1

2. 9 . a ) / t - ^'(1
li) A / 'n 1 >h !)t;;,ir<^«' n . $ •(>«}<). / V. ^ or 0 . 0 2 5 ; f is 0 , 5
l> $ 1 / i)U(l f ? ' . T . » 1 % ' y>3% or 0 . 0 3 5 . f 10 A '.h(iO( 1 1 (() i f ' 3 ) i ( i '41
4 (ton, i t I " 0 A «>43
A 10 3<}'i i n v e s t m e n t is $ 3 6 4 5 .
! I,,, u i i u . r •^.i!u.- ',i 111.- t : S B w o u l d b e $ 1 6 2 0 0 . l akiV-J C ' ^ ' i ' = • ^ is 0.5
7 . a l T h e y will b e e q u a l , e . g . , T h e p r i n c i p a l , i n t e r e s t r a t e ,
A ^ ''.^!.2 Of)
a n d t e r m a r e e q u a l . B o t h e a r n $ 3 0 0 in i n t e r e s t .
! h e hiiuiv v a l u . « .4 I o l o y . f . n v e s t m e n t is $ 3 5 5 2 . 5 0 .
b | N o . e . g . . W i t h s i m p l e i n t e r e s t , t h e r e is n o a d v a n t a g e t o
Of>|,;itfii,n(> I h o (lihr-ron'.f
h a v i n g it p a i d m o r e o f t e n .
:if,.13 53!)2 fT) 32 30
c) e.g.. T h e y m a y need t h e interest m o n e y to pay a
f j i " , i r r ( will h VJ'- i ' J . ' '<<>i«'5 t h a n L a t o y a a f t e r
m o n t h l y bill.
6 months.
b) Desiree; 3645 - 3600 = 45
A , r 1-fM'UO , ,'.%or0.05;fis5 D e s i r e e will e a r n $ 4 5 in i n t e r e s t .
n H, i . n i „ , • t ' ( l ' . , ( 5 ) ) I . i t o f a: 3552,50 - 3500 = 52.50
L a t o y a will e a r n $ 5 2 . 5 0 in i n t e r e s t .
'jV„ - . . v e s t m e n t A is $ 1 2 5 0 0 , Determine the difference;
a ''r.'M.Juo.- , ( . 4 % o r 0 , 0 1 4 ; f is 1 0 5 2 , 5 0 - 4 5 = 7.50
•)(10)) L a t o y a will e a r n $ 7 , 5 0 m o r e in i n t e r e s t t h a n D e s i r e e .
c) Desiree:
4 1.1.'.-'
45
fh s>ui, <4 : i v e s t m e n t B ! S $ 1 1 4 0 0 . r a t e of r e t u r n = ^
C our. . .% 1.9% o r 0 . 0 1 9 ; f is 7
rate of return = 0.0125 or 1.25%
))(7))
e ' ^ A vO Latofa:
tui.jrr H.uf i n v e s t m e n t C i s $ 1 1 3 3 0 . 52.50
rate of r e t u r n = ^
r) I ' , J . i h i.i«o . =' 0 5 % o r 0 . 0 1 0 5 ; f is 8
r.' 5 .nof.C • . )0..05)(8)) rate of r e t u r n = 0 . 0 1 5 o r 1.5%
L a t o y a ' s r a t e of r e t u m is h i g h e r t h a n D e s i r e e ' s r a t e
l i n ; f u t u n - v ' ^ . u . _ of i r . v e s t m e n t D i s $ 1 0 8 4 0 ,
of r e t u r n ,
f i..<r 'JU .^f'•' r Ht l i o n t y v a l u e t o l e a s t : I n v e s t m e n t A ,
|,M..r^t H • i w e - s t m e n t C , I n v e s t m e n t D.
10. A r . pff
b ) Mo M . the- . i i n o u n t of i n t e r e s t n o t e a r n e d in t h e last A is $ 1 3 0 0 0 ; P is $ 1 0 0 0 0 ; ris 6 . 5 % or 0.065
1 s yci.ir IS i n s i i l l . c k - n t t o c h a n g e r a n k i n g s .
15 0 0 0 - 10 0 0 0 + ( 1 0 0 0 0 ) ( 0 . 0 6 5 ) ( f )
| , , v - Jfii-f I i l"JiO s e m i - a n n u a l l y , s o f = 5 1.5 o r 3 . 5 .
5000=650f
f , S . 1 T " J 0 0 . .% 3 " / - o r 0 . 0 5 ; f is 3,5
f=7.69
4 ,oO(.0^ ~ 031(3.5))
It will t a k e S h a u n 8 y e a r s t o e a r n e n o u g h m o n e y t o
A - /on
make the down payment.
I h e t u i u i e <.aiue o l - w e s t m e n ^ A I • '1. i i 7 f - 0 ,
B . I n v e s t m e n t is p a i d a n n u a l l y . St. I H. 2 or 8. 11. a ) 7 = P ( 1 + rt)
Pi' $ 1 0 0 0 0 ; r is 1.4%> o r 0.0 U , i 3 A is $ 2 0 0 0 0 ; r is 3 . 2 % o r 0 . 0 3 2 ; t is 5
4 . ifiiMM)f1 + ( 0 . 0 1 4 ) ( 8 ) ) 20 000 = P(1 + (0.032)(5))
/ t - i l 120 20 000 = 1.16P
T t i e f u t u r e v a l u e of i n v e s t m e n t B is $ 1 1 1 2 0 ,
P = $17 241.38
I n v e s t m e n t is p a i d q u a r t e r l y , s o f is 7 1.5 o r 5 , 5 ,
b) 7 = P + Prt
P i s $ 1 0 0 0 0 ; r i s i r / o o r 0 , 0 1 9 ; f is 5.5
A is $ 2 5 0 0 0 ; P i- % 1 / 24 i .3; r is 3 . 2 % o r 0 . 0 3 2
4 = 10 0 0 0 ( 1 + ( 0 , 0 1 9 ) ( 5 . 5 ) ) 2 5 0 0 0 = 17 2 4 1 3 8 + ( 1 7 2 4 1 3 8 ) ( 0 . 0 3 2 ) ( f )
^ = 11 0 4 5 7758.62 = 551.72f
T h e f u t u r e v a l u e of i n v e s t m e n t C is $ 1 1 0 4 5 . f = 14,06
D. I n v e s t m e n t is p a i d a n n u a l l y , s o f is 8 ^ 2 o r 6.
It will t a k e a b o u t 14.1 y e a r s f o r t h e G I C t o b e
P ib $ 1 0 0 0 0 ; r is 1 . 0 5 % or 0 . 0 1 0 5 ; t is 6
$25 000.
A - 10 000(1 + (0,0105)(6))
A " 10 630
T h e i u t u r e v a l u e of i n v e s t m e n t D is $ 1 0 6 3 0 .
C h a p t e r 1: F i n a n c i a l M a t h e m a t i c s : i n v e s t i n g M o n e y
1-2

3. A is $9400; P is $4700; t is L e s s o n 1.2: E x p l o r i n g C o m p o u n d interest
page 19
i • , • )
E v e : P is $3000: r is 4 % o r 0.04- t is 5
71 •-- Zmm^ + (0.04)(5))
A = mm
• '• • '''-^ ' '(•-,<•-,. ( •-. .Oe • '.'.e"> .,(t f,
I >l»ly f - • ,|,ir,jl (...,.. -i i , H , , , ]^
I n e a n n u a l i n t e r e s t rate is 12,5%,
I.-. >. + rt)
A = P(i +(0.04)(1)) •
Pm $ 4 7 0 0 ; r i s 12,5% o r 0,125- f is 16
•'••''•'•=1' ''>"iiiU .. ., . I
71 = 4700(1 +(0,125K16))
A = 14100 • '• "• - ' i!'!. e> I' - . r , I
v s . ., .. • • ,
table to organize t h e answers.
T h e v a l u e o f t h e i n v e s t m e n t w o u l d b e $14 100.
• 'ff-'V I t'nmApM ( I f " " j Yc-ar e i . e » i , 4 . i . .
1 3 . a ) T h e s l o p e o f tho g r a p h w o u l d i n c r e a s e if t h e , < , 'AU'.-) . 0
[ j _ _ _ T 3 ^
11
interest rate i n c r e a s e d . F o r e x a m p l e , t h e i n v e s t m e n t
VVP"..'
c u r r e n t l y earr n t e r e s t e v e r y 3 y e a r s , s o it h a s a j ' ' .1 ;e, "
> '.i-l "O
l4 13374^59^
slope of ^ . A steeper graph with a slope of | would .•'"'JO
3 6 4 0 QR
m e a n t h e i n v e s t m e n t is e a r n i n g $2 o f i n t e r e s t e v e r y Lciiiy s i r i v e s i m e n t is w o r t h $3649.96 a f t e r 5 y e a r s
3 y e a r s . T h i s c o u l d o n l y h a p p e n if t h e i n t e r e s t rate C a l c u l a t e t h e d i f f e r e n c e in interest
increased, 3649.96 ^ 3600 = 49.96
b | e.g.. Similar: T h e y h a v e t h e s a m e intere-st r a t e T h e L a r r y ' s i n v e s t m e n t e a r n e d $49.96 m o r e in i n t e r e s t
situations a r e represented by a linear relation that slopes t h a n E v e ' s b e c a u s e his i n v e s t m e n t e a r n e d i n t e r e s t
u p w a r d t o t h e right. T h e g r a p h s relate m o n e y t o t i m e o n t h e p r i n c i p a l a n d o n t h e a c c u m u l a t e d interest.
The graphs have the same slope.
Different; They have different principals. T h e interest = P ( 1 + rt)
g r a p h s t a r t s a t (0, 0) w h i l e t h e i n v e s t m e n t g r a p h s t a r t s a t $6500; r is 5 . 1 % o r 0.051 - f is 4
e a y n t A : P is
(0, 3 ) . T h e i n v e s t m e n t g r a p h s h o w s t h e v a l u e o f t h e )500(1 + (0.051 K 4 ) )
i n v e s t m e n t a n d t h e interest w h i l e t h e i n t e r e s t g r a p h o n l y '826,00
s h o w s o n l y t h e interest,
n v e s t m e n t in a c c o u n t A is w o r t h $ 7 8 2 6 0 0
after four years,
1 4 . T h e C S B G r a h a m b u y s in y e a r 1 is i n v e s t e d f o r
5 y e a r s . T h e C S B h e b u y s in y e a r 2 is i n v e s t e d f o r OmTus^I ''^ "'^ °'
4 y e a r s , a n d s o o n . T h e C S B h e b u y s in y e a r 5 wili b e ^ = P(1 + ( 0 . 0 4 8 K 1 ) )
i n v e s t e d f o r 1 year. D e t e r m i n e t h e y e a r l y v a l u e o f t h e C a l c u l a t e t h e interest 4 t i m e s , u s i n g t h e v a l u e o f 4
SB then add the values together as the new value of P for each new year Use a
t a b l e t o o r q a n i z e t h e answerc;
• ' I I r. e > , . ; , . ; , ,
YoiJi _ Principal f$|
I ' feer Y'im_ ind V a l u e ($) _ » _ _^ t350fj ( l i i 0012 00^
/_ „ _ 0312 Os)
jfi/b _ _ j / 1 3 3 9H f4r,ih2.)]^
1 1 of '7 _ _ J nai 33 7fsi0.77
I 1.32
i h e i n v e s t n f c i i l in d o c o u n i b is w o r t h $ 7 8 4 0 7 7
! 190 after four years. Sydney should choose account B
Ic.fal
3370 b e c a u s e it will e a r n m o r e interest.
f . M h a i i ' s ir.ve'4m*-nt will h e w o r t h 3 5 5 7 0 d f t c i 5 y e a r s
1 5 C a r o l e ' s a c c o u n t p a y s i n t e r e s t d a i l y s o s h e will e a r n 3. a ) e . g . , n o it is n o t p o s s i b l e t o tell a s t h e
86 days of interest w h e n s h e withdraws h e r m o n e y p n n c i p a l s , interest rates, a n d t i m e l i n e s all differ
C o n v e r t 8 6 d a y s t o a f r a c t i o n o f a year- b H = P(1+rf)
86 I n v e s t m e n t A : initial P is $ 6 0 0 0 ; r is 1.2% o r
= 0,235... 0 . 0 1 2 ; f is 1 (for 4 y e a r s ) .
3D5
A = P{1 + rt) 4 - P ( 1 < (0.012)(1))
P is $ 2 4 0 0 0 ; r is 5 , 2 % o r 0.052- t is 0 2 3 5 Principal ($1
^ = 2 4 000(1 +(0.112X0,235,..)) 600CL00 0072.00
^ = 24 294.049... OOTZOC)^ 614486^
Carole withdrew $24 294.05 w h e n s h e closed her 6144J6 ~
savings account. 6218.60 6293.23
Return o n investment A- 6 2 9 3 2 j 6000 = 293.23
F o y n d a t i o n s o f M a t h e m a t i c s 12 S o l u t i o n s M a n y a l
1-3

4. Investment B^/'..;.,-.(HH. M S n - e c u m i ID '.4.".
-J. I) a}
4 5,l)fifl(1 i n j 0 4 M ' 4 i
By llu- till.; t'l /;•• sni- .evf .ifin-nl 'Aiil d o u b l e in
K.J,',i„"'n.nv.e,t,ur..t|> n/'.Cl ',f)lHI 14nu 10 n u VH.»-.
l„vestmcmt (4-n.lMH r. $ muO. . ,s f.%-.r 0 ue. / r. ! I • 4('t.-nnin. > tht; .-ic teal 4 o u ! ) ! i i i o t : m e :
»
(foi I. y<vir4 -fi,, p,it»to,.li - f f n u o ! h . - . i n ; » i o n n t e r e s t r a t e i s 6 . 8 % .
/, /'(I . n) ubi{1)) Iht; .,orrip()ui.4in.| p.-oud i;. oiu.n.i', o r o n c e p e r y e a r .
I Year P r i n c i p a l ($) Ycar^endValijod) _ r i i f ' tenn (in v«v)f 4 ''• •"T.ntiwn
' 4(100 UO 1440 no _ |ip-fuh!i.-volu*-!' d.,Ml4-3''fH.T. or $14 0 0 0 .
I 0 1 (in 44n4 40 _ _ III.: f>n;iiK.!.i! aj»o!.e;sii-)n on m y c a l c u l a t o r :
! iv.Av
I • ; .f-in4 4 0 > A/U4 Of. Ihf. hn.ihliinj tin«; H' 3 4 yt: »% w h i c h IS v e r y
i ' i ' V t . ' l f4 ' , S()44 01 f j , , . . . ; !o 14. . I ' d S ' i f - ' ) ! i<> -.U v'.virs.
1 n n | i } n" ^ j ')-^0? 4(1
i if " i S44'«iO ' 4 4 / 4 ua
Hv 4..- 'U! ..1 . . , t h e i n v e s t m e n t will d o u b l e in
!.'( uif.i (••->, ipv» ' . l i u i - i i l
C n,,/4U4 4UiiU e,7''e.4
i. 1 V(>-»>-.
! -e 4 , r . tn< (|a, s5«%-l r e i n m e<' i i r / e ' . ' - i ' X ' i ' i
! , d.'i.'O! ..^'h J a c t u a l d o u b l i n g t i m e :
. ,r,.!. S850. T h e a n n u a l i n t e r e s t r a t e is 9 . 2 % .
« . . s s c „ . 1.3: C o m p o u n d I n t e r e s t : F u t u r e V a l u e , f h e c o m p o u n d i n g p e n o d is m o n t h l y , o r 12 t i m e s
| - M t | e 5fl per year.
The term (in years) is unknown.
1(2)
T h e f u t u r e v a l u e is d o u b l e $ 8 5 0 . o r $ 1 7 0 0 .
I used the financial application o n my calculator:
T h e d o u b l i n g t i m e is 7 5 6 y e a r s , w h i c h is v e r y
d o s e t o t h e e s t i m a t e of 7 , 8 3 y e a r s .
Row:
cl ''' ''o15...
1 = 0.341, ' 15,6
13.2 U s i n g t h e rule o f 7 2 , it t a k e s 4 . 6 2 y e a r s f o r t h e
R o w 3: f =
_., i n v e s t m e n t t o d o u b l e in v a l u e .
T h e p n n e i p a l is 3 1 / 3 0 0 .
I = 3.3 T h e a n n u a l i n t e r e s t r a t e is 1 5 . 6 % .
3 5 3 T h e c o m p o u n d i n g p e n o d is w e e k l y , o r 5 2 t i m e s p e r
(365)
Row 4: i = — ' 12 I
3oO year.
I = 0.009, T h e term (in years) is unknown.
T h e f u t u r e v a l u e is d o u b l e $ 1 2 5 0 0 , o r $ 2 5 0 0 0 .
I = P(1 + , f 1 used the financial application on my calculator;
T h e d o u b l i n g t i m e is 4 . 4 5 y e a r s , w h i c h is v e r y
P = 520; f = 4 . 5 % compounded monthly.
close to t h e estimate of 4.62 years.
1= 2 : ^ = 0.003 7 5 ; f = 8 y e a r s . n = 8 . 1 2 = 96
d) 1 1 = 2 6 . 6 6 6 . . .
A = 520(1 + 0 . 0 0 3 7 5 ) *
U s i n g t h e rule of 7 2 , it t a k e s 2 6 . 6 7 y e a r s for t h e
4 = 744.829...
T h e f u t u r e v a l u e of t h e i n v e s t m e n t is $ 7 4 4 . 8 3 . i n v e s t m e n t t o d o u b l e in v a l u e .
744 829 - 520 = 224.829... T h e p n n e i p a l is $ 4 0 0 0 0 .
T h e t o t a l i n t e r e s t e a r n e d o n t h e i n v e s t m e n t is $ 2 2 4 . 8 3 . T h e a n n u a l i n t e r e s t r a t e is 2 . 7 % .
b) P = 1400; r = 8.6% c o m p o u n d e d semi-annually, T h e c o m p o u n d i n g p e r i o d is s e m i - a n n u a l , o r
2 times per year.
j ^ M ¥ . = 0 0 4 3 ; f = 15 y e a r s , n = 15 • 2 = 3 0 The term (in years) Is unknown.
2 T h e f u t u r e v a l u e is d o u b l e $ 4 0 0 0 0 , o r $ 8 0 0 0 0 .
^ = 1400(1 + 0 . 0 4 3 ) ^ ° I used the finaneial application on my calculator:
A - 4 9 5 0 5 9 3 .. T h e d o u b l i n g t i m e is 2 5 . 8 5 y e a r s , w h i c h is c l o s e t o
T h e f u t u r e v a l u e of t h e i n v e s t m e n t is $ 4 9 5 0 . 5 9 .
t h e e s t i m a t e of 2 6 . 6 7 y e a r s .
4950 593 -^1400 = 3550.593...
T h e t o t a l i n t e r e s t e a r n e d o n t h e i n v e s t m e n t is $ 3 5 5 0 . 5 9 .
1.4

5. i i | a ) T h e p r i n c i p a l is $ 7 0 0 0 T h e a n n u a l i n t e r e s t r a t e is 6 J % T h e c u r r e n t v a l u e of t h e i n v e s t m e n t w i t h i n t e r e s t
s 38, T h e c o m p o u n d i n g p e r i o d is a n n u a l , o r o n c e p e r i.r!'|. n,.irfihl-/ I , S I S Of,..- •! i
y e a r . T h e t e r m (in y e a r s ) is 3 5 , ! ) ! ' . i!- , i ' !l.f. ri«( 1
The future value is unknown.
Vf .11 . Animal Monthly
A = P(1 + /)"
A = 7000(1 + QMm'f eotijijoiiriciisig •.ooipf.ondmc}
A B9 9 9 9 , 0 0 7 , , , n {)
T h e f u t u r e v a l u e of t h e i n v e s t m e n t is $ 6 9 9 9 9 0 1 . ca.n 4 < / ' n v h 3M
69 999.007... ^ 7000 = 62 999.007... ,•() I 'M) • " ^i3.'' 0 4
T h e t o t a l i n t e r e s t e a r n e d is $ 6 2 9 9 9 . 0 1 . f.3 j f / , '/
b ) T h e p n n e i p a l is $ 8 5 0 . T h e a n n u a l i n t e r e s t r a t e is 9 . 2 % ••4:i> 3 0 jJ ^ n/4,'. i f .
s o / = 0 0 9 2 . T h e e o m p o u n d i n g p e r i o d is m o n t h l y . T h e 7o,-/ 4s I ; ; n 4 i lT.
t e r m (in y e a r s ) is 2 0 , ll :3' ih '• 1 03/ o f
»
n = 2 0 • 12 = 2 4 0
The future value is unknown
A = P(1 + if
12 00C
A = 850(1 + 0,092f^'^
A = 5314.630... I- i-f -
T h e f u t u r e v a l u e o f t h e i n v e s t m e n t is $ 5 3 1 4 , 6 3 . ? < »s: . • monthly
5314.630... - 8 5 0 = 4464.630... compounding
T h e t o t a l i n t e r e s t e a r n e d is $ 4 4 6 4 6 3 . • annual
c ) T h e p n n e i p a l is $ 1 2 5 0 0 . ' •')'.'i
T h e a n n u a l i n t e r e s t rate is 1 5 . 6 % s o i = 0 1 5 6 .
< >••• > ]
T h e c o m p o u n d i n g p e n o d is w e e k l y , o r 5 2 t i m e s p e r y e a r .
Xhrt t ^ r n - " e a r s ) is 5. c
0
le is unknown.
c) A s c o m p o u n d i n g frequency increases, interest
• ih.( 260 rate g r o w t h i n c r e a s e s .
0.156)-
1 h' : A-j-K .'.'i.je of t h e i n v e s t m e n t is $ 2 7 2 3 6 . 5 8 ,
2 / ' 4 3 3 3 - 1 t 5 0 0 = 14 7 3 6 . 5 8
I h c S 4 c 4 , n 4 . . iSt e a r n e d is $ 1 4 7 3 6 . 5 8 . U s i n g t h e rule o f 7 2 . it will t a k e 15 y e a r s for P a r k e r
41 inr< p r ; i i , o ( . il is $ 4 0 000. t o d o u b l e his i n v e s t m e n t .
i n e a n n u a l i n t e r e s t r a t e is 2 . 7 % s o i = 0 . 0 2 7 Using a financial application:
T h e c o m p o u n d i n g p e r i o d is s e m i - a n n u a l , o r 2 t i m e s p e r y e a r T h e p n n e i p a l is $ 6 0 0 0 .
T h e t e r m (in y e a r s ) is 8. T h e a n n u a l i n t e r e s t rate is 4 . 8 % .
n = 8 • 2 = 16 T h e c o m p o u n d i n g p e r i o d is a n n u a l , o r o n c e p e r y e a r .
The future value is unknown. The term (in years) is unknown.
A = P(1 4 if T h e f u t u r e v a l u e is d o u b l e $ 6 0 0 0 . o r $ 1 2 0 0 0
46
A = 40 0 0 0 ( 1 + 0 . 0 2 7 ) ' T h e d o u b l i n g t i m e is 1 4 , 7 8 y e a r s , w h i c h is c l o s e t o
A = 49 5 7 2 . 4 1 0 . .. t h e e s t i m a t e of 15 y e a r s .
T h e f u t u r e v a l u e of t h e i n v e s t m e n t is $ 4 9 5 7 2 . 4 1
49 572.41 - 40 000 = 9572.41
T h e t o t a l i n t e r e s t e a r n e d is $ 9 5 7 2 . 4 1 . 15 - 10 = 5
U s i n g t h e rule o f 7 2 , P a r k e r w o u l d b e a b l e t o b u y
4. a)
his m o t o r c y c l e 5 y e a r s s o o n e r .
P r i n c i p a l ($) 3000 "ooot) ~ Using a financial application:
Interest Rate per A n n u m ^0.09 ^ 0.09 T h e p n n e i p a l is $ 6 0 0 0 .
Periods per Year f 12 T h e a n n u a l i n t e r e s t r a t e is 7 . 2 % .
V a l u e at E n d o f Y e a r T h e c o m p o u n d i n g p e n o d is a n n u a l , o r o n c e p e r y e a r .
o" 3000 ou"" 3000 00 The term (in years) is unknown.
3885.09 T h e f u t u r e v a l u e is d o u b l e $ 6 0 0 0 , o r $ 1 2 0 0 0 .
3925 93
T h e d o u b l i n g t i m e is 9 . 9 7 y e a r s , w h i e h is c l o s e t o
H 6 .3031.30 313/.66
9 t h e e s t i m a t e of 10 y e a r s .
6515.68 6723.37
12^ 14.78 - 9.97 = 4.81
8437.99 8798 51
13 P a r k e r w o u l d b e a b l e t o b u y his m o t o r c y c l e
10 9 2 7 . 4 5 " ' 11 5 i 4 " r <
4.81 years sooner.
18 14 151.36 1 13 0 6 7 9 1 J
T h e c u r r e n t v a l u e of t h e i n v e s t m e n t w i t h i n t e r e s t
c o m p o u n d e d a n n u a l l y is $ 1 4 1 5 1 . 3 6 .
F o u n d a t i o n s o f M a t h e m a t i c s 12 S o l u t i o n s M a n u a l
1-5

6. 8. F o r $ 1 0 0 0 t o g r o w v 3 n . 0 0 0 . it w o u l d d o u b l e
6. T h e p r i n c i p a l is $ 2 5 0 0 0 0 .
T h e a n n u a l interest r a t e is 3 . 8 % . four times.
T h e c o m p o u n d i n g p e r i o d is s e m i - a n n u a l , o r 2 t i m e s p e r
a) X 4 = 48
y e a r . T h e t e r m (in y e a r s ) is 1. ' 6
r? = 1 • 2 = 2 U s i n g t h e rule o f 7 2 . it w i l l t a k e 4 8 y e a r s f o r $ 1 0 0 0
The future value is unknown. t o g r o w t o $ 1 6 0 0 0 at a n i n t e r e s t rate of 6 %
/ I = P ( 1 + if c o m p o u n d e d annually.
A - 2 3 0 onn(i I 0 033)-'
A - e s n nou oof! b) I ? x 4 = 24
' 12
1 IIP volur .)? Ih<- hu-st mod a f t e r o n e y e a r is $ 2 5 9 6 9 0 . 2 5 ,
U s i n g t h e rule o f 7 2 , it w i l l t a k e 2 4 y e a r s f o r $ 1 0 0 0
' notjoo . " , 0 f.9(i'OS 0590.25
t o g r o w t o $ 1 6 0 0 0 at a n i n t e r e s t rate o f 1 2 %
ii„- Pu'.l tinid l'.:c. 39')',in 2 5 a v a i l a b l e e a c h y e a r . c o m p o u n d e d annually.
Bool? A IS- o''.-- 'on! !S $20 000, 9. T h e i n t e r e s t g r o w s by a bit m o r e t h a n $ 5 0 e a c h
I ht .in.0.4 in>--i' '.I oti? I ; 6,6%.
year s o I will g u e s s that the pnneipal w a s $ 8 0 0 .
1,,^ ( f.p'.e . 1 " . . ! i s a n n u a l , or o n c e per year.
Use this value to d e t e r m i n e the interest rate.
' n- i I.''' y .>• i ''
T h e p n n e i p a l is $ 8 0 0 .
n = 2 •1 = 2
The annual interest rate is unknown.
; I, '.j!'!!'• •'I <•/».'*•.' wn.
T h e c o m p o u n d i n g p e r i o d is a n n u a l , o r o n c e p e r y e a r .
- /< i T h e t e r m (in y e a r s ) is 3.
/ O C)w{n 5 The future value $966,36.
I I used the financial application on my calculator;
/ e s t m e n t is $ 2 2 7 2 7 . 1 2
t h e a n n u a l i n t e r e s t rate is 6 . 5 % .
22 7 20 000 = 2727,12
T e s t t h e s e v a l u e s t o s e e if t h e y p r o d u c e t h e
2727.12 c o r r e c t v a l u e of t h e i n v e s t m e n t in y e a r 2 .
o; • = 0.136 356,.
20 000 T h e p n n e i p a l is $ 8 0 0 .
Th -l of r e t u r n o n t h e B a n k A i n v e s t m e n t is 13.64¥o.
.O T h e a n n u a l i n t e r e s t rate is 6 . 5 % .
S - i r * R: T h e p r i n c i p a l is $ 2 0 0 0 0 . T h e c o m p o u n d i n g p e r i o d is a n n u a l , o r o n c e p e r y e a r .
luai i n t e r e s t rate is 6 , 5 5 % . T h e t e r m (in y e a r s ) is 2.
%i. . . o m p o u n d i n g p e r i o d is s e m i - a n n u a l , o r 2 t i m e s p e r y e a r . The future value is unknown.
T h e t e r m (in y e a r s ) is 2 . I used the financial application on my calculator;
n = 2 • 2 = 4 t h e f u t u r e v a l u e of t h e i n v e s t m e n t is $ 9 0 7 , 3 8 0 . .
Ttie future value is unknown. If the p n n e i p a l is $ 8 0 0 a n d t h e a n n u a l i n t e r e s t rate
A = P ( 1 + if is 6 . 5 % . t h e v a l u e o f t h e i n v e s t m e n t a f t e r t w o y e a r s
A = 20 0 0 0 ( 1 + 0 . 0 6 5 5 ) ^ IS $ 9 0 7 . 2 8 , w h i c h is t h e v a l u e g i v e n in t h e t a b l e .
A = 22 751,540... T h e i n t e r e s t rate o f 6 . 5 % a n d p r i n c i p a l of $ 8 0 0 a r e
T h e f u t u r e v a l u e of t h e i n v e s t m e n t is $ 2 2 7 5 1 . 5 4 . correct.
22 751.54 - 20 000 = 2751.54
10. F i r s t f o u r y e a r s : T h e p n n e i p a l is $ 4 0 0 0 0 .
R a t e of r e t u r n ; = 0-137 5 7 7 . . . T h e a n n u a l i n t e r e s t rate is 4 . 8 % .
T h e c o m p o u n d i n g p e n o d is s e m i - a n n u a l , o r t w i c e p e r y e a r .
T h e rate of r e t u r n o n t h e B a n k B i n v e s t m e n t is 1 3 . 7 6 % .
B a n k C : T h e p n n e i p a l is $ 2 0 0 0 0 . T h e t e r m (in y e a r s ) is 4 . n = 4 • 2 = 8
T h e a n n u a l i n t e r e s t rate is 6 . 5 % . lt,o future value is unknown.
T h e c o m p o u n d i n g p e r i o d is q u a r t e r l y , o r 4 t i m e s p e r y e a r . A--.PI1+0"
A ~ 40 000(1 + 0.048)"
T h e t e r m (in y e a r s ) is 2. n = 2 - 4 = 8
A 4 0 357.032...
T h e future value is unknown.
T h e v a l u e o f t h e i n v e s t m e n t a f t e r four y e a r s is
A = P ( 1 + if
$48 357.03
A = 20 000(1 + 0.065)"
L a s t t w o y e a r s : T h e p n n e i p a l is $ 4 8 3 5 7 . 0 3 .
A = 22 752.779...
T h e a n n u a l i n t e r e s t rate is 6 % .
T h e f u t u r e v a l u e o f t h e i n v e s t m e n t is $ 2 2 7 5 2 . 7 8 .
T h e e o m p o u n d i n g p e r i o d is a n n u a l , o r o n c e p e r y e a r .
22 752.78 - 20 000 = 2752.78
T h e t e r m (in y e a r s ) is 2 ,
R 3 , e of r e t u r n : 0.137 639.. 0 = 2-1=2
The future value is unknown.
T h e rate of r e t u r n o n t h e B a n k C i n v e s t m e n t is 1 3 . 7 6 % . A = P(1 + if
T h e rates from greatest to least return on investment are A = 4 8 3 5 7 . 0 3 2 . ..(1 + 0 . 0 6 ) '
6.5%. c o m p o u n d e d quarterly (13.76%, Bank C), 6.55%. A = 54 333.962. .
compounded semi-annually (13.75%, Bank B), and T h e t o t a l v a l u e o f t h e i n v e s t m e n t a f t e r six y e a r s is
6.6%. compounded annually (13.63%, Bank A).
$54 333.96,
C h a p t e r 1: F i n a n c i a l M a t h e m a t i c s : I n v e s t i n g M o n e y
1-6

7. F i r s t f o y r y e a r s : T h e p r i n c i p a l ^, ]. i ...e. i i | e.g., T e n y e a r o p t i o n :
T h e a n n u a l i n t e r e s t r a t e is 9 % .
Advantage __^isad¥antage
T h e c o m p o u n d i n g p e r i o d is semi-^annual, o r 2 t i m e s p e r y e a r
T h e t e r m (in y e a r s ) is 4 , G I C i n t e r e s t rate is C a n n o t b e n e f i t if b a n k
0 = 4-2 = 8 s e c u r e if b a n k i n t e r e s t interest rates rise.
The future value is unknown,
4 = P(1 + if D o n 4 need to think Cannot reinvest the
A = 1500(1 + 0.09)^ about investment for ten m o n e y for t e n y e a r s .
A = 2133,150... years.
T h e v a l u e o f t h e i n v e s t m e n t a f t e r f o u r y e a r s is $ 2 1 3 3 . 1 5 . Five year twice o p t i o n :
L a s t two y e a r s : T h e p r i n c i p a l is $ 2 1 3 3 , 1 5 . Advatitage Disadvantage
T h e a n n u a l i n t e r e s t r a t e is 1 1 % ,
• -OM h( nefit f r o m h i g h e r W i l l e a r n l e s s i n t e r e s t if
T h e c o m p o u n d i n g p e r i o d is m o n t h l y , o r 12 t i m e s p e r y e a r
terest rates bank interest rates drop
T h e t e r m (in y e a r s ) is 2 .
Jinvesting. after five years.
,i o/ 2-1
nvest money. Interest rates need to
The future value is unknown.
rise o v e r 3 . 2 5 % for total
A = P{1 + if
investment to earn
A = 2133,15(1 + OAlf*
s a m e interest as ten
/I = 2655,407,..
year option.
T h e t o t a l v a l u e o f t h e i n v e s t m e n t a f t e r six y e a r s is $ 2 6 5 5 . 4 1 .
eg.,
1 2 . a | e . g . . T h e h i g h e r i n t e r e s t r a t e is p a y m e n t in
exchange for more time before maturity. f f4tnilar j Different '~
b | i) 1 0 y e a r o p t i o n : T h e p n n e i p a l is $ 5 0 0 0 , Bofh investments pay ! 4 o m p o u n d inten-s?
T h e a n n u a l i n t e r e s t r a t e is 3 . 2 5 % . If.terest a s a p e r c e n t ' •. . - ' e s t m e n t s a l s o p a y
T h e c o m p o u n d i n g p e r i o d is a n n u a l , o r o n c e p e r y e a r . the pnneipal. j i'sorest on previous
T h e t e r m (in y e a r s ) is 1 0 , 1 terest earned.
0 = 1 0 - 1 = 10 b i h investments can npio interest
The future value is unknown. h , calculated using a | estments are easier
71 = P ( 1 + if i^imula. 1 calculate b e c a u s e
A = 5000(1 + 0.0325)'° ly h a v e f e w e r
A = 6884.471.., iables
T h e v a l u e o f t h e i n v e s t m e n t a f t e r t e n y e a r s is $ 6 8 8 4 . 4 7 , Both investments ' T j m p o u n d interest
F i v e y e a r t w i c e o p t i o n : T h e p r i n c i p a l is $ 5 0 0 0 . i n c r e a s e in v a l u e ovet e s t m e n t s i n c r e a s e in
T h e a n n u a l i n t e r e s t rate is 2 , 6 5 % . time. vaiue more rapidly than
T h e c o m p o u n d i n g p e r i o d is a n n u a l , o r o n c e p e r y e a r . simple interest
T h e t e r m (in y e a r s ) is 5. investments wilh the
0 = 5-1=5 ne interest rate.
The future value is unknown.
" - " ' 1 -r if 1 4 . a ) T h e C S B P u d e e n b u y s in y e a r 1 is i n v e s t e d
A 'f»00(1 + 0 . 0 2 6 5 ) ^ for 5 y e a r s . T h e C S B s h e b u y s in y e a r 2 is
A ~ .)t-98.555... i n v e s t e d for 4 y e a r s , a n d s o o n . T h e C S B s h e b u y s
, . J l u e o f t h e i n v e s t m e n t a f t e r f i v e y e a r s is $ 5 6 9 8 . 5 6 in y e a r 5 will be i n v e s t e d f o r 1 y e a r .
R e i n v e s t e d : T h e p r i n c i p a l is $ 5 6 9 8 . 5 6 . Determine the yeady value of the five-year C S B
T h e a n n u a l i n t e r e s t r a t e is 2 . 6 5 % , then add the valuer toqether
T h e c o m p o u n d i n g p e r i o d is a n n u a l , o r o n c e p e r y e a r . P r i n c i p a l (J) ] ^ " "^^^0 ~ ^
T h e t e r m (in y e a r s ) is 5, f^A^l^jA f^ate p e r ^ A n j i n m " "lJJ.02tl^ f
0 = 5-1=5 P e n o d s per Year _ p
The future value is unknown. V a l u e at E rid of Year _ [ ^ ~ ~
A - P(1 + if
1 „ _^ J I y i i i f
A 5698.56(1 + 0.0265)^
A - 6494.706,., „ J „ ^ 529 64 "
_ ^ ^ ^ ^ 545 IJ ~
f h e v a l u e o f t h e i n v e s t m e n t a f t e r t e n y e a r s is $ 6 4 9 4 . 7 1 .
I ^ 561 03
e.g., Interest rates are c o m p o u n d e d annually, interest
r a t e s r e m a i n t h e s a m e in 5 y e a r s , c a n r e i n v e s t all 0 ^ ^ 5 7 / 42 '
$ 5 6 9 8 . 5 6 in 5 y e a r s . lotnl ^ ?Z^Z-8i^
T h e v a l u e of P u r i e e n ' s i n v e s t m e n t a f t e r f i v e y e a r s
is $ 2 7 2 7 8 1 .
I
F o u n d a t i o n s o f M a t h e m a t i c s 12 S o l u t i o n s M a n u a l
1-7

8. D Mv i n v r s t i n m i t m o l u r o d allot 5 years: $5725.96
Year Savings (S)
'"Piinr.ipal ($) '><)() 20 1 I 5000 00
j |i4cror.t pft Annum
2012 148 '
I 14-ri(Kis |)f;r Y i ; a i 2
5 2 8 0 6()
i V n l u e at t i i 4 ..f Y e a r
2/2/ ai Ai I 1 !)42f) BSf
1 ' 1 to ;>
594 24 4015 55// 19
r.
f , l f 44 2 0 I <. 5>25 96
_ /
1441 4 1 E . I r o l ' o d ,i 1 M y i n v o s t i i i o n l ' s i n t e r e s t rate
^ ~8 ZZZZZZ
y 447 94 d f n n;o%f:d l o 1 / 5 ' 4 . .
: ' 10 hbi] H'y F I i n v . v d f d III t n e 5 yf.'or ' - . I ' . <.nce m o r e , s i n c e it
4 H / 7 4^. l i , o . inn hifjlu.-i m i e n ' O f fnf(;
' ' " k.r«!
i i r ' n v f . . t f ' d m y ^.ovirvj'- $ 4 / 2 - ' i 4 6 , a n d i n v e s t e d
; h . , v . i i u t ; n-i irr./f-.'r.sf-if a f t n i t:;n y e a r ;
$ 5 0 0 0 per yeat s i n c e my init.ai i n v e s t m e n t f o r a
$5877.96. total of $ 3 0 725.96.
G . I r e a c h e d m y g o a l o f 1 m i l l i o n in 2 1 2 8 , w h e n I
I'J (-nvinan; ».f of j «; . c - f.ui 4-'• i. >st 4f p: • < (4
?
:,',< 4 . i v w i | . / 5 - . n t...ii I ' • 1 .' iti« ,<MV nt would be 139.
• r n ; , r. 4 -/(-..iis ! f"- 4 i . f H ; .i< i=c . . i , . , y.Mn> . . ^ u i ' 'f: H. I n o t i c e d t h a t w h e n i n v e s t i n g in a 5 - y e a r G I C , I
-ijfi. f.,j - 1 .', fifitif.if
- )!-•/»•!•./ '"AO 7 n n r , would not invest more m o n e y for another 5 years.
• c-;cin<<i. i r - i . ; •! K uf 4i.- ! > - V C J I .Kjpussl . it ' '7 W h e n I c o m p a r e d t h e r e s u l t s o f a 1-year G I C o v e r
4, . m n n , i ' i 4 4i^; d« t . ' r n l - 4 I ' H J i ' . O d 10 y e a r s a n d a 5 - y e a r G I C o v e r 10 y e a r s , I n o t i c e d
that t h e 5-year G I C performed better than the
, i'.HH ip ii f 4 ; _ 1-year G I C o n l y in t h e 1 0 t h y e a r . T h e r e f o r e , a
s t r a t e g y t h a t w o u l d r e s u l t in t h e l e a s t a g e t o r e a c h
r c n » ! 4 s pof 7fM< m y g o a l w o u l d h a v e m e i n v e s t $ 5 0 0 0 p e r y e a r in a
I V'5lu( . i l l m l <•> fe.Jf 1-year G I C f o r t h e first 5 - 9 y e a r s t o i n c r e a s e m y
4<ji h . f a i Will- principal as fast as possible. T h e n , I would invest
i i ' ^ p o r i t ".1 in a s e r i e s o f 5 - y e a r G I C s until I r e a c h e d m y g o a l ,
noi' Of- since t h e 5-year G I C yields a higher interest rate.
^ " 1} : tiC 4 on I. T h e o u t c o m e o f t h e d i e roll a f f e c t e d m y
VIJ4V ni] investment m u c h more than the strategy I w a s
L Z Z Z Z I ^ ^
i422 42 using, since m y interest rate w o u l d s o m e t i m e s dip
i 4 , ^ 5 2 2 5-'
I r 4 ? f.4
^ 5168 14» b e l o w 0, m e a n i n g m y i n v e s t m e n t lost v a l u e .
J . Since savings accounts, GICs, and Canada
The w of 4 nv"^- - n - f - o i t n t - n t a
Savings B o n d s d o not have negative interest rates,
$5168.65.
it w o u l d m a k e s e n s e n o t t o let t h e r a t e s g o b e l o w
z e r o . M o r e o v e r , t h e B a n k o f C a n a d a a d j u s t s its
History C o n n e c t i o n , p a g e 32
i n t e r e s t r a t e b a s e d o n i n f l a t i o n , t o k e e p inflation
A . r . p . a t t h e s t a r t o f t h e 1 9 5 0 s , t h e i n t e r e s t rate w a s
between 1 % and 2 % . Depending on the
2 5 % . T h e i n t e r e s t rate i n c r e a s e d s l o w l y o v e r t h e first
i n v e s t m e n t , it w o u l d b e r e a s o n a b l e n o t t o let r a t e s
half o f t h e d e c a d e a n d , b y t h e e n d o f t h e d e c a d e , it w a s
for the C a n a d a Savings Bond go below 0 . 5 % or
5%. e x c e e d 5 % . A n y d i e roll t h a t w o u l d r e s u l t in t h e
B. T h e best time to invest w o u l d h a v e b e e n at the e n d of C S B r a t e g o i n g o u t s i d e t h e s e limits c o u l d b e
t h e 1 9 5 0 s , w h e n t h e i n t e r e s t rates w e r e a t t h e i r h i g h e s t considered as "no changeT
for t h e d e c a d e . T h e s e modifications could m e a n that I could reach
my investment goal faster, since I would never lose
Applying Problem-Solving Strategies, page 33 m o n e y in a n y p e r i o d . O n t h e o t h e r h a n d , it c o u l d
A I will start s a v i n g in 2 0 1 6 . a l s o r e s u l t in r e a c h i n g m y i n v e s t m e n t g o a l m o r e
B. Research results s l o w l y , s i n c e t h e i n t e r e s t rate o n t h e C S B c o u l d
never exceed 5%.
K. M y m o d i f i e d r u l e s a c t u a l l y d e c r e a s e d t h e a g e a t
Savings accouru , 1 bO%_
which I reached the goal. Following the investment
GIC (1-year) ' 1 45%
s t r a t e g y o f a 1-year G I C f o r t h e first 10 y e a r s , t h e n
GIC (Ssyearl 2 /5%_
a 5 - y e a r G I C t h e r e a f t e r , I r e a c h e d m y g o a l in 2 0 7 6 .
Canada Savings Bond 0.65%
when I would be 87.
All t h e s e i n v e s t m e n t s c o m p o u n d d a i l y .
C . I c h o s e t o i n v e s t m y $ 5 0 0 0 in t h e 5 - y e a r G I C .
Chapter 1 Financial Mathematics: Investing Money
1-8

9. T o r e a c h m y g o a l at a m o r e r e a s o n a b l e a g e t h e r u l e s
7!'.r/ 2 . •. . e r m i n e t h e a n n u a l i n t e r e s t r a t e
c o u l d b e c h a n g e d to a l l o w a l a r g e r i n v e s t m e n t e a c h y e a r
• v a l u e is $ 2 0 0 0 .
O r . t h e r u l e s c o u l d b e c h a n g e d t o a l l o w a n i n v e s t m e n t of
•nterest rate is unknown.
$ 5 0 0 0 in o n e 5 - y e a r G I C e a c h y e a r , i n s t e a d of e v e r y
5 years. ' •• e n d i n g p e n o d is s e m i - a n n u a l , o r
/ear.
0 f I. >..- (.., y e a r s ) is 5
Lessoo i 4 • ^^npounci Interest: P r e s e n t ¥alye alue is $ 3 5 0 0 .
page 40
' ' m.; . , 4 c u l a t o r , t h e a n n u a l i n t e r e s t r a t e is 1 1 . 5 % .
1 . I n v e s t m e n t B will r e q u i r e a g r e a t e r p r e s e n t v a l u e t o be 11'.,%'} 3. I ) . i . j r m i n e t h e p r e s e n t v a l u e .
i n v e s t e d b e e a u s e t h e c o m p o u n d i n g f r e q u e n c y in l e s s
than for investment A,
P = ^ ^ ^
(To/)" ^ = 0 . 0 0 6 . 0 = 48
v a l u e is $ 8 2 5 4 . 4 8 .
Ut.vj 4 I )• i--rmine t h e i n v e s t m e n t t e r m ,
I n v e s t m e n t A : A = 10 0 0 0 , i = ^ , o = 120
12 v a l u e is 6 0 9 . 3 5 .
10 0 0 0 i t e r e s t r a t e is 1 3 . 6 % .
l d i n g p e r i o d is a n n u a l , o r o n c e p e r
0.05
1+
12 years) is unknown.
Iue is $ 1 0 0 0 0 0 . 0 0 .
P 6071 61
< 'rK, .;culator, t h e t e r m o f t h e i n v e s t m e n t is
T h e p r e s e n t v a l u e o f i n v e s t m e n t A is $ 6 0 7 1 . 6 1 .
' ' 40 y e a r s .
I n v e s t m e n t B : A = 10 0 0 0 , / = 0 . 0 1 2 5 . n = 4 0
f't'^-vi 5 o"- - o m i n e t h e a n n u a l i n t e r e s t r a t e
T h e p r e s e n t v a l u e is $ 1 6 1 5 0 . 0 0 .
(1 + 0 . 0 1 2 5 ) * The annual interest rate is unlinown.
P 6084.13 T h e c o m p o u n d i n g p e r i o d is m o n t h l y , o r 12 t i m e s p e r
year.
T h e p r e s e n t v a l u e o f i n v e s t m e n t B is $ 6 0 8 4 . 1 3
T h e t e r m (in y e a r s ) is 2.
Investment B requires a higher present value.
T h e f u t u r e v a l u e is $ 2 3 5 0 0 . 0 0 .
S' i o v t - s f . j t e n t A :
/-• -O ,1,'.' U s i n g m y c a l c u l a t o r , t h e a n n u a l i n t e r e s t r a t e is 1 8 . 9 % .
P 6071.61
M 4 . a) P
^ = 1647_,,
/' A = 260 000, I = 0.085. o = 20
p^_250J)00_
I n v e s t m e n t B:
A _ 10 0 0 0 (1+ 0.085)"°
P " 6084.13 P 48 904.097. „
M a c should invest $48 9 0 4 . 1 0 n o w to h a v e
643..
$ 2 5 0 0 0 0 in 2 0 y e a r s .
T h e f u t u r e v a l u e t o p r e s e n t v a l u e ratio for I n v e s t m e n t A b) 250 000 ^ 48 904.10 = 201 095,90
IS 1 . 6 4 7 . . . a n d f o r i n v e s t m e n t B is 1 . 6 4 3 . . . T h e i n v e s t m e n t wiil e a r n $ 2 0 1 0 9 5 . 9 0 in i n t e r e s t in
b) T h e investment with annually c o m p o u n d e d interest 20 years
w o u l d h a v e a h i g h e r ratio b e c a u s e t h e i n t e r e s t r a t e is
h i g h e r a n d t h e p r i n c i p a l is l o w e r . W i t h a 6 % i n t e r e s t rate 5. a ) T h e p r e s e n t v a l u e is $ 9 0 0 0 .
c o m p o u n d e d annually and a future value of $10 000 the The annual interest rate is unknown.
present value must be $5583.95. Since the principal'is T h e c o m p o u n d i n g p e r i o d is q u a r t e r i y , o r 4 t i m e s
l o w e r t h a n b o t h i n v e s t m e n t A a n d B, t h e ratio will be per year.
higher. T h e t e r m (in y e a r s ) is 2 ,
T h e f u t u r e v a l u e is $ 1 7 0 0 0 ,
3. R o w 1 : D e t e r m i n e t h e p r e s e n t v a l u e J o s e p p i e w o u l d n e e d a n a n n u a l interest rate of
3 3 . 1 % t o m e e t his g o a l . T h i s is not r e a s o n a b l e .
P = ^ Current interest rates for savings a c c o u n t s are
(1 + / ) " 0 , 5 % t o 1.25%.
A = 2500, / = 0.078, n = 8
T h e p r e s e n t v a l u e is $ 1 3 7 0 . 8 5 .
F o y n d a t i o n s o f M a t h e m a t i c s 12 S o l y t i o n s M a n u a l
1-9

10. b ) T h e p r e s e n t v a l u e is $ 9 0 0 0 ,
Option Rate of R e t u r n
T h e a n n u a l i n t e r e s t rate is 1 2 % .
A 3<384
T h e c o m p o u n d i n g p e r i o d is q u a r t e r l y , or 4 t i m e s per y e a r . (} .124 3 3 3
The term (in years) is unknown. 4 3 1 13 2 2
T h e f u t u r e v a l u e is $ 1 7 0 0 0 . 3 8 9 1 43
0 .',2^. ; r 7 )
U s i n g m y c a l c u l a t o r , it will t a k e J o s e p p i e 5.4 y e a r s t o h a v e 18^108 57
$17 000. 386/,63
f)..;2:!. (4)1
18 132 3 5
A
6. P Opti.;r, B h a s IIlO y r f i o t e s i o 4 e of r r d o n i at 32 3 3 ' 4
(iZTf
Sasha should choose option B so that she earns
A = 17 5 0 t : / o -.'28, o = 2 0
the most interest on her investment,
C l a i r e h a s t o i n v e s t $ 1 0 0 7 3 . 3 9 now t o h a v e $ 1 7 5 0 0 in t e n b) S a s h a w o u l d earn $ 5 8 9 1 . 4 3 on her investment
years. b y c h o o s i n g o p t i o n B.
>hf i>.ir:fi'i s/,m(f i . mknowr}.
T h e a n n u a l inti . -,1 f.J,.- s 4 • ' } % 8 O p t i o n A : e . g . . I n c r e a s e t h e i n t e r e s t rate t o
|„>ii, 4 < ototiK.
% once per year. T fi% in p a r t h) a n d d e c r e a s e t h e i n t e r e s t rate t o
• ill I iMj,>'»
,11 - o >f> >r
. 1 n-y. ii
in. : 41
<3 4 0 !
0 = 6-1=6 P r m o i p a l {%) 10 o<-<; ; 35 o n e
interest Rate ppr u '.7:H o 070 4 01*'
A
Aiimim _ _ ^ _ ;_
(1 + f T
P e r i o d s p e r ~feat^ I '
24 0 0 0 V a l y e at^EncJ o f Y e a r
p =
^ 1 4 101 C4> I • / 3 6 6 6 4 13 3 7 o 4 /
(l + 0.0480f
^ ^ 17 4 4 3 2 ^ " 4 0 106 03_ _i 10 l / 2 ' » j i
P 18 1 1 5 . 2 1 7 . . ,
_6_ ~'6'ik'1i'T 232/907 _ 1 0 i T T +
T h e p r e s e n t v a l u e of o p t i o n A is $ 1 8 1 1 5 , 2 2 .
2 0 2 1 4 «3< ' .-'fl 0^)1 9 0 • / 4 i l 52
Interest e a r n e d : 24 000 18 1 1 5 , 2 2 - 5 8 8 4 , 7 8
41 7 8 0 i 3 ^ ' 2i;4 2 / ' 18 1 0 6 . 4 4
O p t i o n B : T f i e present value is unknown.
T h e a n n u a l i n t e r e s t rate is 4 . 7 5 ° 4 . Ol. Mil
T h e c o m p o u n d i n g p e r i o d is s e m i - a n n u a l , o r 2 t i m e s p e r y e a r .
T h e t e r m (in y e a r s ) is 6 y e a r s .
T h e f u t u r e v a l u e is $ 2 4 0 0 0 , / ' CO' 5
v. ri(.13
1 J'H !
ISOuC
1-CM.n
! i , r. M - i / o r
.(> SCO
P_ p : 443 3 / 1 ,.
4 h o I o / . e r u v . i l u e o f opti<'i« % o 4 4 3 108.57. i'OMiC
I n i e i p s t f n m e d 2 4 0 0 0 ^ 18 103 3 / ^ 5 8 9 1 . 4 3 t r o O . r
O p t i o n C : The present value is unknown.
T h e a n n u a l i n t e r e s t rate is 4 . 7 0 % , Ye.its
T h e c o m p o u n d i n g p e r i o d is q u a r t e r t y , o r 4 t i m e s per y e a r . Valye ot iri¥_estmenti$|
T h e t e r m (in y e a r s ) is 6 y e a r s . (years! 3=) „
T h e f u t u r e v a l u e is $ 2 4 0 0 0 , 0 15 0 0 0 15 0 0 0 T3JJ00
24 J6101:^»t)^!-'^Z i 0 4 ) M ^ [o "^fML.
V 4 T 1 2 8 • 30 100 6 8 ^ 10 172.90
A
1 8 761454 I " 2 ^ 2 79 0:3 16 7 9 3 . 3 1
^ (111)' 1/4^7.52
^ 8 2 0 2T4^83 , 2 6 OOJ .9<T
P 24 0 0 0 _ 21 780 3 3 ^ 3 1 204.27 18 106.44
10
MiS)0470r
P 18 1 3 2 , 3 5 1 . . ,
ifdetesiecimed: 24 0 0 0 - i L35 = 5867.65
Chapter 1: Financial M a t h e m a t i c s : Investing M o n e f
1-10