Question

A sum of INR 15000 is put on compound interest. This sum becomes 2 times in 5 years at this rate. What would the original sum become after 20 years?

• A. 60000
• B. 225000
• C. 140000
• D. None of these

Hint:

When calculating compound interest, remember the formula \( A = P \left(1 + \frac{R}{100}\right)^n \) and take care when working with long periods like 20 years.

Answer 1

The Correct Option is D

Let the principal amount be \( P = 15000 \) INR, and let the rate of interest be \( R \). After 5 years, the sum becomes double, i.e., \( 2P = 30000 \). This shows that the sum grows by a factor of 2 in 5 years. Since the interest is compounded, the formula for compound interest is: \[ A = P \left(1 + \frac{R}{100}\right)^n \] where \( A \) is the amount after \( n \) years. For \( n = 5 \), we have: \[ 30000 = 15000 \left(1 + \frac{R}{100}\right)^5 \] Simplifying, we get: \[ 2 = \left(1 + \frac{R}{100}\right)^5 \] Taking the 5th root of both sides: \[ \left(1 + \frac{R}{100}\right) = \sqrt[5]{2} \] \[ 1 + \frac{R}{100} \approx 1.1487 \] \[ \frac{R}{100} \approx 0.1487 \quad \Rightarrow \quad R \approx 14.87% \] Now, to find the amount after 20 years, we use the compound interest formula again: \[ A = 15000 \left(1 + \frac{14.87}{100}\right)^{20} \] \[ A = 15000 \times (1.1487)^{20} \approx 15000 \times 19.45 \approx 291750 \] Thus, the sum will become approximately 291750 INR after 20 years, but this is not listed as an option. Therefore, the correct answer is (d) None of these.