EXAMPLE PROBLEMS ON SIMPLE INTEREST

Find the simple interest charged when :

Example 1 :

$5000 is borrowed for 1 year at 12% per annum simple interest

Solution :

Principal P = $5000, R = 12%, T= 1 year

Simple interest I = (P × T × R)/100

= (5000 × 12)/100

= 60000/100

= 600

Simple interest for 1 year is $600.

Example 2 :

$2500 is borrowed for 2 years at 8% per annum simple interest

Solution :

P = $2500, R = 8%, T= 2 years

Simple interest I = (P × T × R)/100

= (2500 × 2 × 8)/100

= 40000/100

= 400

Simple interest for 2 years is $400.

Example 3 :

$40000 is borrowed for 5 years at 11% per annum simple interest

Solution :

P= $40000, R = 11%, T = 5 years

Simple interest I = (P × T × R)/100

= (40000 × 5 × 11)/100

= 2200000/100

= 22000

Simple interest for 5 years is $22000.

Example 4 :

$250000 is borrowed for 9 months at 20% per annum simple interest.

Solution :

P = $250000, Rate R = 20%, Time T= 9 months

1 year = 12 months

Time T = 9/12 ==> 3/4

Simple interest I = (P × T × R)/100

= (250000 × 3/4 × 20)/100

= 3750000/100

= 37500

Simple interest for 9 months is $37500.

Example Problems on Finding Amount on Simple Interest

Find the total amount needed to repay a loan of :

Example 5 :

$2400 borrowed for 3 years at 10% per annum simple interest.

Solution :

P = $2400, R = 10%, T = 3 years

Simple interest I = (P × T × R)/100

= (2400 × 3 × 10)/100

= 72000/100

= 720

Simple interest for 3 years is $720.

Total amount = P + I

= 2400 + 720

= 3120

So, total amount is $3120.

Example 6 :

$8000 borrowed for 7 years at 12% per annum simple interest

Solution :

P = $8000, R = 12%, T = 7 years

Simple interest I = (P × T × R)/100

= (8000 × 7 × 12)/100

= 672000/100

= 6720

Simple interest for 7 years is $6720.

Total amount = P + I

= 8000 + 6720

= 14720

So, total amount is $14720.

Example 7 :

$7500 borrowed for 2 1/2 years at 8% per annum simple interest.

Solution :

P = $7500, R = 8%, T = 5/2 years

Simple interest I = (P × T × R)/100

= (7500 × 5/2 × 8)/100

= 150000/100

= 1500

Simple interest for 2 1/2 years is $1500.

Total amount = P + I

= 7500 + 1500

= 9000

So, total amount is $9000.

Example 8 :

$23000 borrowed for 4 months at 15% per annum simple interest.

Solution :

P = $23000, R = 15%, T= 4 months

1 year = 12 months, T = 4/12 ==> 1/3

Simple interest I = (P × T × R)/100

= (23000 × 1/3 × 15)/100

= 115000/100

= 1150

Simple interest for 9 months is $1150.

Total amount = P + I

= 23000 + 1150

= 24150

So, total amount is $24150.

Example 9 :

Kyle borrows $25000 at 6% p.a. Simple interest for 4 years.

(a)  Find the total amount needed to repay the loan.

(b)  Calculate the monthly repayment required to pay this loan off in 48 equal instalments.

Solution :

P = $25000, R = 6%, T = 4 years

Simple interest I = (P × T × R)/100

= (25000 × 4 × 6)/100

= 600000/100

= 6000

Simple interest for 4 years is $6000.

Total amount = P + I

= 25000 + 6000

= 31000

So, total amount is $31000.

(b) Amount is being paid for 48 equal monthly instalments.

$31000 = 48 months

= 31000 ÷ 48

Instalment amount for a month = $645.83

Example 10 :

You deposit $5000 in an account earning 7.5% simple interest. How long will it take for the balance of the account to be $6500?

Solution :

Simple interest I = (P × T × R)/100

Principal = 5000, T = ? and R = 7.5%

Amount = 7500

Principal + interest = 7500

5000 + interest = 7500

interest = 7500 - 5000

interest = 2500

2500 = (5000 x T x 7.5)/100

2500(100) = 5000 x T x 7.5

T = 250000/(5000 x 7.5)

T = 6.6

Approximately 7 years.

Example 11 :

You put $400 in an account. The account earns $18 simple interest in 9 months. What is the annual interest rate?

Solution :

Simple interest I = (P × T × R)/100

P = 400, I = 18, T = 9/12 ==> 3/4

18 = (400 x 3/4 x R)/100

18 = 3R

R = 18/3

R = 6%

So, the annual rate of interest is 6%.