# CLASS-6SIMPLE INTEREST - PROBLEM & SOLUTION

PROBLEM & SOLUTION (SIMPLE INTEREST) -

Example.1) John borrowed \$2000 from a friend at an annual simple interest rate of 8%. He plans to repay the loan in 3 years. Calculate the total amount John will have to repay, including both the principal and the interest.

Ans.) Given:

• Principal (P) = \$2000
• Rate (R) = 8% = 0.08 (as a decimal)
• Time (T) = 3 years

Using the formula for simple interest:-

Simple Interest (SI) = Principal (P) × Rate (R) × Time (T)

Substitute the values: SI = \$2000 × 0.08 × 3 = \$480

OR

8

SI = \$2000 X ------- X 3 = \$480

100

Now, to calculate the total amount to be repaid:-

Total Amount = Principal + Simple Interest Total Amount

= \$2000 + \$480 = \$2480

Total Amount = \$2480

Therefore, John will have to repay a total amount of \$2480, including both the principal and the interest, after 3 years.

In this example, the interest earned is \$480 over 3 years, which is 8% of the initial \$2000 borrowed. This demonstrates how simple interest is calculated and how it contributes to the total repayment amount.   (Ans.)

Example.2) Tom borrowed \$500 from a friend for a period of 3 years at an interest rate of 7% per annum. Calculate the amount of simple interest Tom will have to pay and the total amount he will need to repay at the end of the loan term.

Ans.) Given:

• Principal (P) = \$500
• Rate (R) = 7% per annum (0.07 as a decimal)
• Time (T) = 3 years

Step 1:- Calculate the simple interest using the formula:-

Simple Interest (SI) = Principal × Rate × Time

SI = \$500 × 0.07 × 3 = \$105

OR

7

= \$500 X ------ X 3 = \$105

100

Step 2:- Calculate the total amount to be repaid:-

Total Amount = Principal + Simple Interest Total Amount

= \$500 + \$105 = \$605

Answer: Tom will have to pay \$105 as simple interest, and the total amount he needs to repay at the end of the loan term is \$605.

In this example, the simple interest is calculated as \$105, which is 7% of the initial principal amount of \$500 for a duration of 3 years. The total amount repaid includes both the principal and the interest, resulting in a final payment of \$605.        (Ans.)

Example.3) John borrowed \$2000 from a friend at an interest rate of 8% per year. He needs to repay the loan in 3 years. Calculate the total amount John will have to repay, including the simple interest.

Ans.) Given values:

Principal (P) = \$2000

Rate (R) = 15% per year (0.15 as a decimal)

Time (T) = 5 years

Using the formula for simple interest:-

Simple Interest (SI) = P × R × T

Calculate the simple interest: SI = \$2000 × 0.15 × 5 = \$1500

15

Or,  S.I =  \$2000 × --------- × 5 = \$1500

100

Now, to find the total amount John will have to repay:-

Total Amount = Principal + Simple Interest Total Amount

= \$2000 + \$1500 = \$3500

So, John will have to repay a total amount of \$3500, which includes the principal of \$2000 and the simple interest of \$1500, over the course of 5 years at an 15% interest rate.       (Ans.)

Example.4) Sarah borrowed \$4000 from a friend for a period of 10 years at an annual interest rate of 12%. Calculate the total amount of interest she will have to repay at the end of the loan term.

Ans.) Given values:

• Principal (P) = \$4000
• Rate (R) = 12% = 0.12 (decimal)
• Time (T) = 10 years

Using the formula for simple interest:
Simple Interest (SI) = Principal (P) × Rate (R) × Time (T)

Substitute the values: SI = \$4000 × 0.12 × 10 = \$4800

OR

12

SI = \$4000 X -------- X 10 = \$4800

100

So, Sarah will have to repay a total of \$480 in interest at the end of the 10-years loan term.

To find the total amount she needs to repay (principal + interest):

Total Amount = Principal + Simple Interest Total Amount

= \$4000 + \$4800 = \$8800

Therefore, the total amount Sarah needs to repay at the end of the loan term is \$8800, which includes the initial \$4000 principal and \$4800 in interest.             (Ans.)

In this example, the problem involved calculating the simple interest and the total amount to be repaid based on the given principal, interest rate, and time period. This is a basic scenario, but it showcases how simple interest works in real-life situations.