Learning Outcomes:: Solution

Learning Outcomes:
At the end of this module, the students should be able to:
1. Solve problems involving simple interest and simple discount.

2. Differentiate compound interest from simple interest.
3. Solve present value and amount at compound interest.
4. Calculate credit card transactions.
5. Develop mathematical skills in the financial aspects and endeavors in life.
SIMPLE INTEREST
Interest is the fee charged for the use of borrowed money. It is normally a
percentage of the amount borrowed.
Interest that is computed only on the principal amount and is paid at the end of the
loan period is called Simple Interest.
Simple interest (𝐼) depends on three factors:

Principal (𝑃) - the amount of money borrowed or the capital invested
Interest rate (𝑟) - express in percent charged in a specified period of time
Time or Term (𝑡) - the duration on which the principal amount is invested or loaned.
The formula for computing simple interest is:

𝐼 = 𝑃𝑟𝑡
If the given time is expressed in:

a. years - I = P • r • number of years
number of months
b. months - I=P • r • 12
c. days
number of days
 Ordinary Interest Io = P • r • 360
number of days
 Exact Interest Ie = P • r • 365
Example:
1. Given: P = ₱ 20 000
r = 4% = 0.04
t = 2 years
Find: I
Solution: I = Prt
I = ( ₱ 20 000 ) ( 0.04 ) ( 2 )
𝐈 = ₱ 1 600
2. If Christine borrowed ₱ 50 000 from the bank at an interest rate of 10%, how
much is the interest in 9 months?
Given: P = ₱ 50 000
r = 10% = 0.10
t = 9 months
Solution: I = Prt
9
I = ( ₱ 50 000 ) ( 0.10 ) ( 12 )
𝐈 = ₱ 3 750
3. Find the ordinary and exact interest on ₱ 15 000 at 4% simple interest for 45
days.
Given: P = ₱ 15 000
r = 4 % = 0.04
t = 45 days
Solution: Io = Prt
45
Io = ( ₱ 15 000 ) ( 0.04 ) ( 360 )
𝐈𝐨 = ₱ 75.00
Ie = Prt
45
Ie = ( ₱ 15 000 ) ( 0.04 ) ( 365 )
𝐈𝐞 = ₱ 73.97
4. Find the interest earned if ₱ 5 000 is invested at 13% simple interest for 90
days.
Given: P = ₱ 5 000
r = 13 % = 0.13
t = 90 days
Solution: I = Prt
90
I = ( ₱ 5 000 ) ( 0.13 ) ( 360)
𝐈 = ₱ 162.50
Note: If the type of interest is not specified in any problem, always use
ordinary interest (Banker’s Rule).
At the end of the term of a loan transaction, the borrower pays back the
principal amount together with the interest. This amount is called final amount
or maturity value ( F ).
F=P+I or F = P + Prt
F = P ( 1 + rt )
Example:
1. Agnes borrowed ₱ 35 000 from a lending firm that charges 5 ½ % interest
rate. How much will she pay after 3 months?
Given: P = ₱ 35 000
r = 5 ½ % = 0.055
3
t = 3 months = 12
Solution: F = P ( 1 + rt )
3
= ₱ 35 000 [ 1 + (0.055) (12) ]
𝐅 = ₱ 35 481.25
2. Find the interest and maturity value if ₱ 20 000 is borrowed at 12 ½% simple

interest for 4 years.
Given: P = ₱ 20 000
r = 12 ½ % = 0.125
t = 4 years
Solution: I = Prt
I = ( ₱ 20 000 ) ( 0.125 ) (4)
I = ₱ 10 000
F=P+I
F = ₱ 20 000 + ₱ 10 000
𝐅 = ₱ 30 000
There are cases that the principal amount, rate of interest and the time are
missing. In this instance, we can derive the other formulas.
I I I F
r = Pt t = Pr P = rt or P = 1+ rt
Example:
1. Given: I = ₱ 8 000
r = 8% = 0.08
t = 2 years
Find: P
I
Solution: P = rt
₱ 8 000
P = ( 0.08 ) ( 2 )
𝐏 = ₱ 50 000
2. How much should be invested today in a fund that pays 5% simple interest in
order to have ₱ 50 000 in 3 years?
Given: F = ₱ 50 000
r = 5% = 0.05
t = 3 years
F
Solution: P = 1+ rt
₱ 50 000
P = 1+ (0.05 ) ( 3)
𝐏 = ₱ 43 478.26
3. Karlo borrowed ₱ 25 000 from a bank. He paid an interest of ₱ 1 200 for 3

months, at what rate was the interest charged?
Given: P = ₱ 25 000
I = ₱ 1 200
t = 3 months
I
Solution: r = Pt
₱ 1 200
r= 3
( ₱ 25 000 ) ( )
12
𝐫 = 0.192 = 19.2%
4. How long will it take for ₱ 35 000 to earn ₱ 4 500 if the rate of interest is 8%?
Given: P = ₱ 35 000
I = ₱ 4 500
r = 8% = 0.08
I
Solution: t = Pr
₱ 4 500
t=(
₱ 35 000 ) ( 0.08 )
t = 1.60714… years
𝐭 = 1 year, 7 months, 9 days
Note: 1.60714… = 1 year
.60714… x 12 months = 7.28571… or 7 months
.28571… x 30 days = 8.5714… or 9 days

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Learning Outcomes:

At the end of this module, the students should be able to:

1. Solve problems involving simple interest and simple discount.

Simple interest (𝐼) depends on three factors:

The formula for computing simple interest is:

If the given time is expressed in:

2. Find the interest and maturity value if ₱ 20 000 is borrowed at 12 ½% simple

3. Karlo borrowed ₱ 25 000 from a bank. He paid an interest of ₱ 1 200 for 3

Note: 1.60714… = 1 year

.60714… x 12 months = 7.28571… or 7 months

.28571… x 30 days = 8.5714… or 9 days

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