Compound interest is interest that is calculated on the initial principal and also on the accumulated interest from previous periods. It is calculated at regular intervals called conversion periods. The document provides formulas and examples for calculating compound interest, principal amounts, and rates of return in scenarios involving different interest rates, time periods, principal amounts, and maturity values. Sample calculations are shown for computing maturity values, determining the principal needed to reach a future value, and calculating interest earned over time at various compounding frequencies.

1. Compound Interest
Reference: Mathematics of Investment, Winston
Sirug
Dianne Tricia M.
Iniego
Patricia Manansala
Kim Lao
Debbie Mendrano

2. Compound Interest
Compound Interest – is the interest
procedure in which interest is periodically
calculated and added to the principal.
 The time interval between succeeding
interest calculations is called the
conversion period.
 The Nominal interest is the stated annual
interest rate on which the compound
interest calculation is based.
 The Periodic Interest Rate is the rate of
interest earned in one conversion period.


3. Compounding Frequencies and
Periods
Compounding or
conversion
frequency
No. of compounding
or conversions per
year
Compounding or
conversion period.
Annual
1
1 year
Semi-annual
2
6 months
Quarterly
4
3 months
Bi-monthly
6
2 months
Monthly
12
1 month

4. P = Principal amount of the loan or
investment
J = Nominal interest rate
m = Number of conversion per year
t = Time period (term) of the loan or
investment
i = Periodic interest rate
I = Amount of interest paid or received
F = Maturity value of the loan or investment

5. Formulae
F=P(1+i)ˆn
 P = F/(1+i)ˆn
 I = F-P
 j = m(n√F/P-1)

n = tm
i = j/m

6. Computing the Maturity Value
What will be the maturity value of
12, 000 pesos invested for 4 years
at 15% compounded quarterly?
Given: P = 3,000 pesos, t = 4 years
m = 4, n = tm = 4(4) = 16
j = 15% = 0.15, i = j/m = 0.15/4 =
0.0375
1.

7. The maturity value would be
….
F=P(1+i)ˆn
= 12,000(1+0.0375) ˆ16
=12,000(1.0375) ˆ16
=12,000(1.802227807)
=21,626.73368
=21, 626.73 pesos


8. Computing the Principal
Amount
1. What amount must be invested now
in a savings account earnings 9%
compunded quarterly to accumulate
a total of 21,000pesos after 4¾
years?
Given: j = 9% = 0.09, m = 4, F =
21,000
T = 4¾years = 4.75 years,
n = tm =4.75(4), i = j/m = 0.09/4 =
0.225

9. Solution:
P = F/(1+i)ˆn
=21,000/(1+0.0225)ˆ19
=21,000/(1.0225)ˆ19
=21,000/1.526170367
=13,759.931691
=13,759.93 Pesos

10. 2.
Mrs. Sirug wants to provide a
200,000pesos graduation gift for her
daughter Sofia. She is now 16 years
old, and she would like the fund to be
available by the time she is 20. She
decides on an investment that pays
10% compounded quarterly. How
large must the deposit be?
Given: F = 200,000, t = 4 years, j = 10%0.10
m = 4 , n = tm = 4(4) = 16,
i = j.m = 0.10/4 = 0.025

11. Solution
P = F(1+i)ˆ-n
=200,000(1+0.025)ˆ-16
=200,000(1.025) ˆ-16
=200,000(0.6736249335)
=134,724.99pesos
(Mrs. Sirug should deposit
134,724.99pesos in order to grow as
much as 200,000pesos after 4 years.)


12. Computing the Compound
Interest
Find the interest earned at the end of
4 years if 36,700pesos is invested at
12% compounded bimonthly.
Given: P = 36,700, t = 4years, m=6
j = 12% = 0.12, n = tm = 4(6) = 24,
i = j/m = 0.12/6 = 0.02
1.

13. Solution:
F = P(1+i)ˆn
= 36,700(1+0.02)ˆ24
=36,700(1.02)ˆ24
=36,700(1.608437249)
=59,029.65Pesos
I = F-P
= 59,029.65 – 36,700
= 22,329.65 Pesos
The interest earned is 22,329.65

14. Computing the Compound
Interest Rate
The maturity value of a five year,
7,000pesos compound interest
investment certificate was
9,427.99pesos. What quarterly
compounded nominal interest rate
did the investment certificate
earned?
Given: t=5years, P = 7,000pesos, m =
4
n = tm = 5(4) = 20, F = 9,427.99pesos
1.

15. Solution:
j = m(n√F/P-1)
= 4(20√9,427.99/7,000-1)
=4(20√1.346855714-1)
=4(1.0115000027-1)
=0.06 or 6%
