Tom lends $21,567 to his neighbor Fred on October 15, 2015. Tom expects Fred to pay the
principal and simple interest at 15% to fully settle the debt on February 3, 2016. How much will
Tom receive? (1 year = 365 days)
Given:
P = $21,567
r = 15% = 0.15
t = 111/365
F=?
Solution:
October 2015
November 2015
December 2015
January 2016
February 2016
=
=
=
=
16
30
31
=
31
=
3
111days
F = P(1 + rt)
F = 21,567[1 + (0.15) × (
111
)]
365
𝐅 = $𝟐𝟐, 𝟓𝟓𝟎. 𝟖𝟏
Mr. Urbina makes an initial investment of $15,000 for five years. Find the value of the investment
after the five years if the investment earns a return of 20% compounded annually.
Given:
P
= $15,000
r
= 20% compounded annually
t
= 5 years
A
=?
Solution:
A
= P (1+r)^t
A
= $ 15,000 (1 + 0.20/1)^(5)
A
= $ 15, 000 (1.20)⁵
A
= $ 15, 000 (2.48832)
A
= $ 37, 3248
Compound Interest Semi- annually
If the compound interest on ₱ 12000 for the period of 1 ½ years at the rate of interest 15% per
annum, what if the interest is compounded half yearly?
Given:
Principle
Rate of interest
Time
P
R
t
t
= ₱ 12000
= 15%
= 1 1/2
= 3/2 years
= 3/2 × 2= 3 years (interest is compounded half yearly)
Solution:
A
= P (1+ R) ^t
= 12000(1+ 15) ^3
= 12000(1.15) ^3
= 12000× (1.520875) ^3
= ₱ 18,250.5
CI
= A−P
= ₱ 18,250 − ₱ 12000
= ₱ 6,250.5
So, if the interest is compounded half yearly, the result will be ₱ 6,250.5
Joy is first-year student, and she wants to invest her ₱ 75,000 before she graduates at a nominal
interest rate of 8%, compound quarterly. How much will her investment be worth in 4 years?
Given:
A
=?
P
= ₱ 75,000
r
= 8% = 0.08
t
= 4 years
Solution:
A
= P (1+r/4)^4t
A
= ₱ 75,000 (1+0.08/4)^(4)(4)
A
= ₱ 75,000 (1+0.02)¹⁶
A
= ₱ 75,000 (1.02)¹⁶
A
= ₱ 75,000 (1.372785705)
A
= ₱ 102,958.93
Let's consider Gwen's plan to start a business and examine her cash flow using a diagram. In
order to initiate her business venture, she requires an initial capital of 10, 000 pesos. To secure
this capital, Gwen decides to borrow money from a bank that offers a loan with a 5% annual
interest rate, and she agrees to make monthly payments. After a year of running her business, she
makes arrangements to repay the loan to the bank
Given:
P
= 10, 000
r
= 5%
= 0.05
t
= 1 years
Where:
 M is the monthly payment.
 P is the principal loan amount (initial capital), which is 10,000 pesos in
this case.
 r is the monthly interest rate, which is the annual interest rate divided
by 12 (since there are 12 months in a year).
So,

0.05
12
n is the total number of payments, which is the loan term in months. In
this case, it's 12 months.
Now, you can plug these values into the formula:
Solution:
A
= Pr/ [1- (1 + r)^-t]
A
= 10000 (0.05) / [1-(1 + 0.05)^-1]
A
= 500/ 1- 0.9524
A
= 500/ 0.0476
A
= 10, 504.20
Monthly payment
10, 504.20/12
= 875.35
Shorter method:
𝑃 ∗ 𝑟 ∗ (1 + 𝑟) 𝑛
𝑀=
(1 + 𝑟) 𝑛 − 1
0.05
0.05
10,000 ∗ ( 12 ) (1 + 12 ) 12
𝑀=
0.05
(1 + 12 ) 12 − 1
𝑴 = 𝟖𝟕𝟓. 𝟑𝟓