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An amount of Rs. 43,892 is lent to each of two persons for 3 years. One at the rate of 30% simple interest and the other at the rate of 30% compound interest, compounded annually. by what percentage will the simple interest be less than the compound interest received in this 3 - year duration (correct to one decimal place)?
1. 24.7%
2. 23.8%
3. 22.7%
4. 25.7%

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Correct Answer - Option 1 : 24.7%

Given:

The principal of each person is Rs.43892.

The first on SI at rate of 30% for 3 years.

The second on CI at rate of 30% for 3 years.

Formula Used:

SI = P × R × T/100

Amount = P[1 + R/100]n

CI = Amount - Principal

Calculation:

The principal of each person is Rs.43892.

The first on Simple Interest at rate of 30% for 3 years.

Simple Interest = 43892 × 30 × 3/100 = Rs.39502.8

The second on Compound Interest at rate of 30% for 3 years.

Amount = 43892[1 + 30/100]3

⇒ 43862 × 130/100 × 130/100 × 130/100

⇒ Rs.96364.81

Compound Interest= 96364.81 - 43892 = Rs.52472.81

The difference between Compound Interest and Simple Interest = Rs.12970.01

The percentage = 12970.01/52472.81 × 100 = 24.7%

∴ The percentage simple interest be less than the compound interest is 24.7%. 

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