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%
1. 24.7%
2. 23.8%
3. 22.7%
4. 25.7%
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%.