- The document discusses different cash flow patterns including single amounts, annuities, and mixed streams. - It then provides examples of calculating future values of cash flows using compound interest formulas, including deposits into money market accounts and evaluating annuity streams. - The key considerations are determining the present and future values, interest rates, and time periods in order to select the more attractive cash flow option.

1. Q1 Difine and differentiate among the three basic patterns of cash flow?
• Single amount – A lump-sum amount either currently held or expected at some future
date.
• Annuity – A level periodic stream of cash flow. We will work with annual cash flow.
• Mixed stream – A stream of cash flow that is not an annuity; a stream of unequal
periodic cash flows that reflect no particular pattern.
Q2 Assume a firm makes a $ 2500 deposit into its money maker account. If this account is
currently paying 0.7% what will the account balance be after 1 year?
Here, Pv= 2500, r=.7% or .7/100 , t= 1 year.
Then,𝐹𝑉 = 𝑃𝑉(1 + 𝑟) 𝑡
= 2500(1+.7/100)^1
= $ 2517.5 (ans)
Q3. Ramesh Abdul wishes to choose the better of two equally costly cash flow streams:
annuity X and annuity Y. X is an annuity due with a cash inflow of $9,000 for each of 6
years. Y is an ordinary annuity with a cash inflow of $10,000 for each of 6 years. Assume
that Ramesh can earn 15% on his investments.
a. On a purely subjective basis, which annuity do you think is more attractive?
Why?
b. Find the future value at the end of year 6, FVA6, for both annuity X and
annuity Y.
c. Use your finding in part b to indicate which annuity is more attractive. Why?
Compare your finding to your subjective response in part a.
Solution:

2. On the surface, annuity Y looks more attractive than annuity X because it provides $1,000 more
each year than does annuity X. Of course, the fact that X is an annuity due means that the $9,000
would be received at the beginning each year, unlike the $10,000 at the end of each year, and this
makes annuity X more appealing than it otherwise would be.
B) Annuity X.
Here , C= 9000, r= 15% or, .15 , n= 6.
Then , Annuity due= FIVA 15%; 6years * pv
= 8.754* ( 1+.15)^1
= 10.0671
Then, annuity is’; c*FIVA
= 9000* 10.0671
= 90603.9
Annuity Y , Here , C= 10000, r= 15% or, .15 , n= 6.
𝐹𝑉 =
𝑐
𝑟
[(1 + 𝑟) 𝑡
− 1]
=
10000
0.15
[(1 + 0.15)6
− 1]
=66666.66 (2.3130 – 1 )
= 87,537.37
C. Annuity X is more attractive because its future value at the end of year 6, FV6, of $90,603.90
is greater than annuity Y’s end-of-year-6 future value, FV6, of $87,540.00. The subjective
assessment in part a was incorrect. The benefit of receiving annuity X’s cash inflows at the
beginning of each year appears to have outweighed the fact that annuity Y’s annual cash inflow,
which occurs at the end of each year, is $1,000 larger ($10,000 vs. $9,000) than annuity X’s
Problem : E4-2 : If Bob and Judy combine their savings of $ 1,260 and $ 975, respectively,
and deposit this amount into an account that pays 2% annual interest, compounded
monthly, what will the account balance be after 4 years?

3. Here, Bob’s deposit Amount $1260 & Zudy’s Deposit amount 975.
Then , the prenciple amount = ( 1260+975)
= $ 2235 their present value.
Interest rate r= 2% or .02/12 , Period 12*4= 48.
We, know, 𝐹𝑉 = 𝑃𝑉(1 + 𝑟) 𝑡
=2235(1+.02/12)^48
= $ 2420.98 (ans)
Problem: E4-3: Gabrielle just won $ 2.5 million in the state lottery. She is given the option
of receiving a total of $ 1.3 million now, or she can elect to be paid $100,000 at the end of
each of the next 25 years. If Gabrielle can earn 5% annually on her investments, from a
strict economic point should she take?
Given That,
C= 100,000 , r=5% or, 0.05 , t= 25 years.
Present value of Annuity =
𝑐
𝑟
[1 − (1 + 𝑟)−𝑡
]
= 100,000/.05 { 1- (1+.05)^-25}
= 2000000 ( 1- 0.29530)
= 1409394.457
$1,409,394 So PV of Future Cash payments at $1,409,394 is higher than $1,300,000 which she is
being offered now. SO she should take the 2nd option.

4. Problem : P4-4 : Use the FVIF in Appendix Table A-1 in each of the cases shown in the table
on the facing page to estimate, to the nearest year, how long it would take an initial deposit,
assuming no withdrawals, a) to double, b) to quadruple. Case Interest rate, i
A 7%, B 40%, C 20% ,D 10%.
Here,
a) To double the initial deposit. It means FV=2, PV=1
b) To quadruple the initial deposit. It means FV=4, PV=1
A) 𝐹𝑉 = 𝑃𝑉(1 + 𝑟) 𝑛
2= 1(1+.07)^n
Or, 1.07^n= 2
Or, n ln1.07= ln2 (taking Ln both the two
sides)
Or, n= ln2/ln 1.07
N=10.24 ( Nearest to 10 Years)
A-2)Another,
𝐹𝑉 = 𝑃𝑉(1 + 𝑟) 𝑛
Or, 4= 1(1+.07)^n
Or, N* ln 1.07= ln 4
Or, n= ln4/ln1.07
N= 20.48 (nearest to 20 years)
B) 𝐹𝑉 = 𝑃𝑉(1 + 𝑟) 𝑛
Or, 2= 1(1+.40)^n
Or, n* ln 1.40 = ln 2
Or n= ln2/ ln 1.40
N=2.060 ( nearest to 2 years)
C) 𝐹𝑉 = 𝑃𝑉(1 + 𝑟) 𝑛
Or, 2= 1(1+.20)^n
Or, n* ln 1.20= ln 2
Or, n= ln 2/ ln 1.20
n= 3.80 ( near to 4 years)
B-2) Another, 𝐹𝑉 = 𝑃𝑉(1 + 𝑟) 𝑛
Or, 4= 1(1+.40)^n
Or, n* ln 1.40 = ln 4
Or, n= ln 4/ ln 1.40
N= 4.12 ( nearest to 4 years)
C-2)another,
4= 1(1+.20)^n
Or, n* ln 1.20= ln 4
Or, n= ln 4/ ln 1.20
n= 7.60 ( near to 8 years)
D) 2= 1(1+ .10)^N
Or, n* ln 1.10= ln 2
Or, n= ln2/ ln 1.10
N=7.27 (near to 7 years)
D-2)Another ,
4= 1(1+.10)^n
Or, n* ln 1.10=ln 4
Or,n= ln4/ln1.10
N=45.54 ( near to 15 years) {AnS}
Problem : P4=5:

5. For each of the cases shown in the following table, calculate the future value of the single
cash flow deposited today that will be available at the end of the deposit period if the
interest is compounded annually at the rate specified over the given period.
Case Single Cash
Flow
Interest
Rate %
Deposit
Period
A $ 200 5 20
B 4500 8 07
C 10000 9 10
D 25000 10 12
E 37000 11 05
F 40000 12 09
Now, In Case A: PV= $200 , r= 5% or 0.05, Period t= 20 Years.
Then, 𝐹𝑉 = 𝑃𝑉(1 + 𝑟) 𝑛
= 200 ( 1+.05)^20
= 530.65
Case B: PV= $ 4500 , r=8% or, .08 , t= 7 Years.
Then , 𝐹𝑉 = 𝑃𝑉(1 + 𝑟) 𝑛
= 4500 ( 1+ .08) ^ 7
= 7712.20
Case C: PV= $ 10000, R= 9%, or , 0.09 , t= 10 years.
Then, FV= 10000 (1+ .09)^10
= 23673.63
Case d: PV= 25000, r= .10 , t=12
Then, FV= 25000(1+.10)^12
=78460.70
Case E: PV=$ 37000, r= .11 , t= 5
Then, FV= 37000( 1+ .11) ^5

6. =62347.15
Case F: PV= 40000, r= .12 , t= 9
Then, FV= 40000( 1+.12)^9
=110923.15
Problem: P5-9
Single Payment Loan repayment A person borrows $200 to be repaid in 8 years with 14%
annually compounded interest. The loan may be repaid at the end of any earliar year with
no prepayment penelty.
a) What amount will be due if the loan is repaid at the end of year 1?
b) What is the repayment at the end of year 4?
c) What amount is due at the end of the eight year?
Solution:
A) Here,
PV= $200, Interest Rate r= 14% or, 0.14, Year t= 1.
Now,
The furmula of Future value ,
FV= 𝑃𝑣(1 + 𝑟)^𝑛
= 200(1+ .14)^1
= 200*1.14
= 228
B) PV= $200 , r= .14, t= 4
𝐹𝑉 = 𝑃𝑉(1 + 𝑟) 𝑛
=200 (1+.14)^4
= 337.79
C) Pv=$200, r=.14 , t= 8 years
FV= 200(1+.14)^8

7. =570.51
Ans: a) $228, b) 337.79 , c) 570.51.