Rashid borrowed a sum of ₹30,240 at 10% p.a., interest compounded annually. If the amount is to be paid back in two equal annual instalments, then the interest paid by him is:

Correct option is D

Given:

Principal (P) = ₹30,240

Rate (R) = 10% p.a.

Time = 2 years

Repayment in 2 equal annual instalments (compounded annually)

Formula Used:

​$$P = \frac{A}{(1 + r)^1} + \frac{A}{(1 + r)^2}$$​​

Where:

P = Present value (loan amount)

A = Annual instalment

r = Rate (as a decimal)

Solution:
Given:

​$$30240 = \frac{A}{1.10} + \frac{A}{(1.10)^2} = \frac{A}{1.10} + \frac{A}{1.21}$$​​

$$30240 = A \left( \frac{100}{110}+ \frac{100}{121} \right) = A \left( \frac{10}{11}+ \frac{100}{121} \right) \\ \ \\30240= A \left( \frac{110+100}{121} \right)\\ \ \\30240=A \times \frac{210}{121}\\ \ \\A = \frac{30240 \times 121}{210} = 17424$$​

Total repayment = 2 × 17,424 = ₹34,848

Interest = Total repayment – Principal = ₹34,848 – ₹30,240 = ₹4,608

Alternate Method:

10% = $$\frac{1}{10}$$ 

A = $$\frac{30240 }{210}\times 242$$ = ₹34,848

Interest = ₹34,848 – ₹30,240 = ₹4,608​