There is an increase of 91% in an amount after 7 years at simple interest. What will be the compound interest of Rs 10,000 on same rate of interest after 2 years ?

Correct option is B

Given:

1. Increase in amount = 91% after 7 years at simple interest.
2. Principal = Rs. 10,000.
3. Time for compound interest = 2 years.
4. Rate of interest (R) is the same for both simple and compound interest.

Formula Used:

1. Simple Interest (SI):
SI = $$\frac{P × R × T}{100}$$​​
2. Compound Interest (CI):
CI = $$P × (1 + \frac{R}{100})^T - P$$​​

Solution:

$$\frac{(P × R × T)}{100} = \frac{91}{100} × P$$​​

1. Find Rate of Interest (R):
Using the simple interest formula:
SI = 91% of Principal (P) = $$\frac{91}{100}$$​ × P
Substituting values:
Cancelling P:
R × 7 = 91 => R = $$\frac{91}{7}$$​ = 13% per annum.

2. Calculate Compound Interest (CI):
Using the CI formula:
​$$CI = 10,000 × (1 + \frac{13}{100})^2 - 10,000$$​​
Simplify:
​$$CI = 10,000 × (1.13)^2 - 10,000$$​​
CI = 10,000 × 1.2769 - 10,000
CI = 12,769 - 10,000 = 2,769

Final Answer:

The compound interest is Rs. 2,769 (Option B).