Simple Interest
Objectives
ØFind simple interest
ØFind the unknown principal, rate, or time
ØFind maturity value
ØSolving real-life problems involving simple ineterest
Annual Simple Interest
ü Principal which is the amount
𝐼! = 𝑃𝑟𝑡
invested or borrowed
ü Simple interest rate, usually
expressed in percent
ü Time or term of loan, in years
where
𝐼! = simple interest
𝑃 = principal
𝑟 = rate
𝑡 = term or time, in years
Annual Simple Interest
Example 1:
Solution:
A bank offers 0.25% annual
simple interest rate for a particular
deposit. How much interest will be
earned if 1 million pesos is
deposited in this savings account
for 1 year?
Given: 𝑃 = 1,000,000
𝑟 = 0.25% = 0.0025
𝑡 = 1 year
Find: 𝐼!
Annual Simple Interest
Find: 𝐼!
Example 1:
A bank offers 0.25% annual
simple interest rate for a particular
deposit. How much interest will be
earned if 1 million pesos is
deposited in this savings account
for 1 year?
𝐼! = 𝑃𝑟𝑡
𝐼! = 1,000,000 0.0025 1
𝐼! = 2,500
The interest earned is
Subject for 20%
withholding tax
PhP2,500.00
Annual Simple Interest
Example 2:
Solution:
Given: 𝑃 = 50,000
How much interest is
charged when P50,000 is borrowed
𝑟 = 10% = 0.10
for 9 months at an annual interest
rate of 10%?
"
𝑡 = #$ year = 0.75 year
Find: 𝐼!
Annual Simple Interest
Example 2:
Find: 𝐼!
How much interest is
charged when P50,000 is borrowed 𝐼! = 𝑃𝑟𝑡
9
for 9 months at an annual interest
𝐼! = 50,000 0.10
rate of 10%?
12
𝐼! = 50,000 0.10 0.75
𝐼! = 3,750
The interest earned is
P3,750.00
Annual Simple Interest
Solution for (a)
Example 3:
Principal (P) Rate (r)
Time (t)
Interest
(a)
2.5%
4
1,500
36,000
(b)
1.5
4,860
250,000
0.5%
(c)
275
500,000
12.5%
10
(d)
If:
𝐼! = 𝑃𝑟𝑡
then : 𝑃 =
%!
&'
#,)**
𝑃 = (*.*$))(.)
𝑃 = 15,000
Annual Simple Interest
Solution for (b)
Example 3:
Principal (P) Rate (r)
Time (t)
Interest
(a)
2.5%
4
1,500
36,000
(b)
1.5
4,860
250,000
0.5%
(c)
275
500,000
12.5%
10
(d)
If:
𝐼! = 𝑃𝑟𝑡
then : 𝑟 =
%!
/'
.,01*
𝑟 = (21,***)(#.))
𝑟 = 0.09 = 9%
Annual Simple Interest
Solution for (c)
Example 3:
Principal (P) Rate (r)
Time (t)
Interest
(a)
2.5%
4
1,500
36,000
(b)
1.5
4,860
250,000
0.5%
(c)
275
500,000
12.5%
10
(d)
If:
𝐼! = 𝑃𝑟𝑡
then : 𝑡 =
%!
/&
$3)
𝑡 = ($)*,***)(*.**))
𝑡 = 0.22 years
Annual Simple Interest
Solution for (d)
Example 3:
Principal (P) Rate (r)
Time (t)
Interest
(a)
2.5%
4
1,500
36,000
(b)
1.5
4,860
250,000
0.5%
(c)
275
500,000
12.5%
10
(d)
If:
𝐼! = 𝑃𝑟𝑡
𝐼! = (500,000)(0.125)(10)
𝐼! = 625,000
Annual Simple Interest
Example 4:
Solution:
When invested at an annual
interest rate of 7%, an amount
earned P11,200 of simple interest
in two years. How much was
originally invested?
Given: 𝑟 = 7% = 0.07
𝑡 = 2 years
𝐼! = 11, 200
Find: 𝑃
Annual Simple Interest
Example 4:
When invested at an annual
interest rate of 7%, an amount
earned P11,200 of simple interest
in two years. How much was
originally invested?
Find: 𝑃
𝐼!
𝑃=
𝑟𝑡
11,200
𝑃=
(0.07)(2)
𝑃 = 80,000
The amount invested is
P80,000
Annual Simple Interest
Example 5:
Solution:
Given: 𝑃 = 500,000
If an entrepreneur applies
for a loan amounting to P500,000
𝐼! = 157, 500
in a bank, the simple interest of
which is P157,500 for 3 years, what
𝑡 = 3 years
interest rate is being charged?
Find: 𝑟
Annual Simple Interest
Example 5:
Find: 𝑟
If an entrepreneur applies
𝐼!
for a loan amounting to P500,000
𝑟=
in a bank, the simple interest of
𝑃𝑡
which is P157,500 for 3 years, what 𝑟 = 157,500
(500,000)(3)
interest rate is being charged?
𝑟 = 0.105 = 10.5%
The bank charged an annual simple
interest rate of
10.5%
Annual Simple Interest
Example 6:
Solution:
How long will a principal
earn an interest equal to half of it
as 5% simple interest?
Given: 𝑃
𝑟 = 5% = 0.05
𝐼! =
Find: 𝑡
#
𝑃
$
= 0.5𝑃
Annual Simple Interest
Example 5:
How long will a principal
earn an interest equal to half of it
as 5% simple interest?
Find: 𝑡
𝐼!
𝑡=
𝑃𝑟
0.5𝑃
𝑡=
(𝑃)(0.05)
𝑡 = 10 years
It will take 10 years for a principal
to earn half of its value at 5%
simple annual interest rate.
Maturity (Future) Value
Many persons or institutions are
interested to know the amount that
a lender will give to the borrower
on the maturity date. For instance,
you may be interested to know the
total amount of money in savings
account after 𝑡 years at an interest
rate 𝑟. This amount is called the
maturity value or future value 𝐹.
𝐹 = 𝑃 + 𝐼!
where
𝐹 = maturity future value
𝑃 = principal
𝐼! = simple interest
Maturity (Future) Value
Many persons or institutions are
interested to know the amount that
a lender will give to the borrower
on the maturity date. For instance,
you may be interested to know the
total amount of money in savings
account after 𝑡 years at an interest
rate 𝑟. This amount is called the
maturity value or future value 𝐹.
Substituting 𝐼! by 𝑃𝑟𝑡 gives
𝐹 = 𝑃 + 𝑃𝑟𝑡
𝐹 = 𝑃(1 + 𝑟𝑡)
Maturity (Future) Value
Many persons or institutions are
interested to know the amount that
a lender will give to the borrower
on the maturity date. For instance,
you may be interested to know the
total amount of money in savings
account after 𝑡 years at an interest
rate 𝑟. This amount is called the
maturity value or future value 𝐹.
𝐹 = 𝑃(1 + 𝑟𝑡)
where
𝐹 = maturity future value
𝑃 = principal
𝑟 = interest rate
𝑡 = term / time in years
Maturity (Future) Value
Example 7:
Note:
Find the maturity value if 1
million pesos is deposited in a bank
at an annual simple interest rate of
0.25% after (a) 1 year and (b) 5
years?
There are two ways to solve the
problem.
Method 1: Solve the simple interest
𝐼! first and then add it to 𝑃, that is
𝐹 = 𝑃 + 𝐼!
Method 2: Use the derived formula
𝐹 = 𝑃 1 + 𝑟𝑡 .
Maturity (Future) Value
Example 7:
Find the maturity value if 1 million pesos is deposited in a bank at
an annual simple interest rate of 0.25% after (a) 1 year and (b) 5 years?
Method 1:
𝐼! = 𝑃𝑟𝑡
𝐼! = 1,000,000 0.0025 1
𝐼! = 2,500
The maturity of future value is
given by 𝐹 = 𝑃 + 𝐼!
𝐹 = 1,000,000 + 2,500
𝐹 = 1,002,500
Method 2:
𝐹 = 𝑃 1 + 𝑟𝑡
𝐹 = 1,000,000 (1 + 0.0025(1)
𝐹 = 1,002,500
The future or maturity value
after 1 year is P1,002,500
Maturity (Future) Value
Example 7:
Find the maturity value if 1 million pesos is deposited in a bank at
an annual simple interest rate of 0.25% after (a) 1 year and (b) 5 years?
Method 1:
𝐼! = 𝑃𝑟𝑡
𝐼! = 1,000,000 0.0025 5
𝐼! = 12,500
The maturity of future value is
given by 𝐹 = 𝑃 + 𝐼!
𝐹 = 1,000,000 + 12,500
𝐹 = 1,012,500
Method 2:
𝐹 = 𝑃 1 + 𝑟𝑡
𝐹 = 1,000,000 ( 1 + 0.0025(5)
𝐹 = 1,012,500
The future or maturity value
after 5 year is P1,012,500
Simple Interest
Seat work
Find the unknown
Principal 𝑃, rate
𝑟, time 𝑡, and interest 𝐼 by
completing the table
Principa
l (𝑃)
Rate
(𝑟)
Time
(𝑡)
Interest
(𝐼)
10,000
8%
15
(1)
(2)
2%
5
10,000
360,000
(3)
2
3,600
500,000
10.5%
(4)
175,500
880,000
9.25%
2.5
(5)