A sum of money increases to ₹7,500 after 5 years and ₹9,200 after 7 years respectively at the same rate of simple interest. Find the approximate rate of interest per annum.

Correct option is D

Given:

Amount after 5 years A₁ = ₹7,500

Amount after 7 years A₂ = ₹9,200

Interest is calculated using Simple Interest (SI)

Formula Used:

Simple Interest Formula:

A = P + SI = P + $$\left(\frac{P \times r \times t}{100}\right)$$​​

where:

A = Amount,

P = Principal,

r = Rate of interest per annum,

t = Time in years.

Solution:

Interest for 2 Years:

Interest for 2 years = A₂ - A₁ = 9,200 - 7,500 = ₹1,700

Annual Interest = $$\frac{1,700}{2}$$​ = ₹850

The amount after 5 years includes the principal and 5 years of interest:

7,500 = P + $$\left(\frac{P \times r \times 5}{100}\right)$$​​

7,500 = P + 5 \times 850

7,500 = P + 4,250

P = 7,500 - 4,250 = ₹3,250

Using the annual interest:

​$$\frac{P \times r}{100} = 850$$​​

​$$\frac{3,250 \times r}{100} = 850$$​​

​$$32.5 \times r = 850$$​​

​$$r = \frac{850}{32.5} \approx 26.2\%$$​​