At what rate of compound interest per annum will a sum of ₹10,000 become ₹11,025 in 2 years?

Correct option is C

Given:

Principal (P) = ₹10,000

Amount (A) = ₹11,025

Time (T) = 2 years
Formula Used:
The formula for compound interest is:

​$$A = P \left(1 + \frac{R}{100}\right)^T$$​​

Where:

A is the amount after interest,

P is the principal,

R is the rate of interest per annum,

T is the time in years.

Solution:

A = 11,025, P = 10,000, T = 2

​$$11,025 = 10,000 \left(1 + \frac{R}{100}\right)^2$$​​

​$$\frac{11,025}{10,000} = \left(1 + \frac{R}{100}\right)^2$$​​

​$$1.1025 = \left(1 + \frac{R}{100}\right)^2$$​​

​$$\sqrt{1.1025} = 1 + \frac{R}{100}$$​​

​$$1.05 = 1 + \frac{R}{100}$$​

​$$0.05 = \frac{R}{100}$$​

R = 5

The rate of compound interest per annum is 5%.

Alternate Method:

P                :                   A

10000             :                11025   (2 years)

$$\sqrt {10000}$$​          :            $$\sqrt{11025}$$  

100                 :                105       (1 year)

Rate = $$\frac {5}{100}\times 100=5\%$$​​