Question

A lady lends two sums each of Rs. 2,500 to two of her friends for 3 years charging 8% p.a. at simple interest for one and the same rate percent at compound interest for the other. Find the difference of interest obtained from the two friends.

a) Rs. 500
b) Rs. 600
c) Rs. 700
d) Rs. 800

Answer 1

The difference in interest obtained from lending Rs. 2,500 at 8% for 3 years as simple interest and compound interest is Rs. 43.04, with simple interest being Rs. 600 and compound interest being Rs. 643.04.cClosest answer is option b.

Step-by-step explanation:

The student's question seeks the difference between the interests obtained through simple interest and compound interest on two sums of Rs. 2,500 each lent for 3 years at a rate of 8% per annum.

Calculating Simple Interest

We use the formula for simple interest (I) = Principal (P) × Rate (R) × Time (T).

For one friend, simple interest on Rs. 2,500 would be:

I = 2,500 × 0.08 × 3 = Rs. 600

Calculating Compound Interest

We use the formula for compound interest on a yearly compounded basis: A = P(1 + R)T

For the other friend, total amount A with compound interest becomes:

A = 2,500(1 + 0.08)3 = 2,500(1.08)3 = Rs. 3143.04

Thus, the compound interest earned is Rs. 3143.04 - Rs. 2,500 = Rs. 643.04.

Difference in Interest

The difference in interest obtained from the two friends is:

Compound Interest - Simple Interest = Rs. 643.04 - Rs. 600 = Rs. 43.04.