The document describes three scenarios where the author's friends and family want to borrow money from the P1,500 the author withdrew from their savings account. In the first scenario, the author's younger sister needs P1,000 for a garage sale and offers to sell the author a bond that the author can keep for a week in return and promises to pay back. In the second scenario, the author's older brother wants to borrow the full P1,500 for a business idea and promises to pay back P1,800 in four weeks. In the third scenario, the author's best friend wants to borrow P1,500 to buy cupcakes to resell at a profit and promises to pay back P1,700

1. General Mathematics

3. Suppose that you withdraw P1,500 from your savings account.
Over the weekend, several people want to borrow money from
you. Read the stories and decide to whom you will lend your
money.

4. Suppose that you withdraw P1,500 from your savings account. Over the weekend,
several people want to borrow money from you. Read the stories and decide to
whom you will lend your money.
1. Your younger sister is having a garage sale. She needs
cash to make change for the day. She will sell you a bond
for P1,000. You will keep the bond for a week and she
promises to pay you back.

5. Suppose that you withdraw P1,500 from your savings account. Over the weekend,
several people want to borrow money from you. Read the stories and decide to
whom you will lend your money.
2. Your older brother has a small business idea but
doesn’t have any money. He wants to borrow your
P1,500 and promises to pay you back P1,800 in four
weeks.

6. Suppose that you withdraw P1,500 from your savings account. Over the weekend,
several people want to borrow money from you. Read the stories and decide to
whom you will lend your money.
3. Your best friend at school, whom you know very well,
wants to borrow your P1,500 to buy cupcakes. She plans
to sell these at a higher price and promises to pay you
back P1,700 in two weeks.

9. Required Formula
Redemption value Rv=Fv(rR)
Coupon payment Cp=Fv(b)
Purchase Price or
value of the bond
p=Rv(1+i)-n +cp
1− 1+𝑖 −𝑛
𝑖
Bond premium Bp=p-Rv
Bond discount Bd=Rv-p

10. Notation Description Definition
Fv
Face value or par value The borrowed principal
stipulated on the bond.
Rv
Redemption date The final amount to be paid on
the redemption date.
Rd
Redemption date The indicated date when the
bond is to be redeemed.

11. Notation Description Definition
rR
Redemption
rate
The interest rate of the bond which will
be applied to the principal in order to
find the redemption value of the bond.
rB
Bond rate The rate at which the bond pays
interest on its face value.
ry
Yield rate The interest rate realized by the
investor or seller on the investment
principal.

12. Notation Description Definition
Bd
Bond
discount
A bond that is bought less than its par
value
cp
Coupon
payment
A periodic interest payment that a
bondholder receives within the bond
period.
b
Periodic bond
rate
The interest rate of the bond per
conversion period. This is obtained by
dividing the bond rate by the number of
conversion
𝑟 𝑏
𝑚
.

13. Notation Description Definition
i
Periodic yield rate This is obtained by dividing
the yield rate by the number
of conversion,
𝑟 𝑦
𝑚
.
Bp
Bond premium A bond that is bought above
its par value.

15. Solution: The problem provides us
Fv=P15,000 rb=0.10 m=4
rR = 1.10 t=8 years b=rb/m=0.10/4=0.025

16. Solution: Substitute
Coupon payment: Cp=Fv(b)
= (15,000)(0.025) = P375
Redemption value: Rv = Fv(rR)
= (15,000)(1.10) = P16,500
Therefore, the coupon payment and redemption value of the bond are P375 and
P16,500, respectively.

18. Solution: The problem provides us
Fv=P20,000 rb=0.14 m=2
rR = 1.08 t=5 years b=rb/m=0.14/2=0.07
ry= 0.06 n=5(2)=10 i=0.06/2 = 0.03

19. Solution: Substitute
Coupon payment: Cp=Fv(b)
= (20,000)(0.07) = P1,400
Redemption value: Rv = Fv(rR)
= (20,000)(1.08) = P21,600
Therefore, the coupon payment and redemption value of the bond are P375 and
P16,500, respectively.

20. Solution: Substitute
Purchase price: p=Rv(1+i)-n +cp
1− 1+𝑖 −𝑛
𝑖
p=(21,600)(1+0.03)-10 +(1,400)
1−(1+0.03)−10
0.03
=
𝑃28,014.71
Therefore, the investor who pays P28,014.71 is investing the money at 6%
compounded semi-annually.

22. Solution: The problem provides us
Fv=P55,000 b=0.08 m=4
ry = 0.12 t=15 years n= 15(4)=60
i=0.12/4=0.03

23. Solution: Since the redemption rate is not given then the
redemption value is equal to the face value.
Coupon payment: Cp=Fv(b)
= (55,000)(0.08) = P4,400

24. Solution: Substitute
Purchase price: p=Rv(1+i)-n +cp
1− 1+𝑖 −𝑛
𝑖
p=(55,000)(1+0.03)-60 +(4,400)
1−(1+0.03)−60
0.03
=
𝑃131,107.80
Thus, the purchase price of the bond is P131,107.80

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