Question

A man lends some money to his friend at 5% per annum of interest rate. After 2 years, the difference between the Simple and the compound interest on money is Rs. 50. What will be the value of the amount at the end of 3 years if compounded annually?

• A. 21325.6
• B. 24512.5
• C. 22252.7
• D. 23152.5

Answer 1

The Correct Option is D

Let's solve the problem step by step.
Given:
- Interest rate \( r = 5\% \) per annum
- The difference between Simple Interest (SI) and Compound Interest (CI) after 2 years is Rs. 50
First, let's denote the principal amount as \( P \).
Simple Interest (SI) for 2 years:
\[ SI = P \times \frac{r}{100} \times t \]
For 2 years, \( t = 2 \):
\[ SI = P \times \frac{5}{100} \times 2 = 0.1P \]
Compound Interest (CI) for 2 years:
\[ CI = P \left(1 + \frac{r}{100}\right)^t - P \]
For 2 years, \( t = 2 \):
\[ CI = P \left(1 + \frac{5}{100}\right)^2 - P = P \left(1.05^2\right) - P = P \left(1.1025\right) - P = 0.1025P \]
Given the difference between CI and SI after 2 years is Rs. 50:
\[ CI - SI = 0.1025P - 0.1P = 0.0025P = 50 \]
\[ P = \frac{50}{0.0025} = 20000 \]
Now, we need to find the amount at the end of 3 years when compounded annually:
\[ A = P \left(1 + \frac{r}{100}\right)^t \]
For 3 years, \( t = 3 \):
\[ A = 20000 \left(1 + \frac{5}{100}\right)^3 = 20000 \left(1.05\right)^3 \]
Calculating \( 1.05^3 \):
\[ 1.05^3 = 1.157625 \]
\[ A = 20000 \times 1.157625 = 23152.5 \]
So, the value of the amount at the end of 3 years if compounded annually is:
Answer: D (23152.5)