Question

A loan is to be returned in two equal yearly instalments. If the rate of interest is 10% p.a., compounded annually, and each instalment is Rs. 5,808, then the total interest charged in this scheme is:
1. Rs. 1,536
2. Rs. 1,632
3. Rs. 1,602
4. Rs. 1,563

Answer 1

Correct Answer - Option 1 : Rs. 1,536

Given:
Amount of each installment = Rs. 5,808
Rate of interest compounded annually = 10%
Number of years (n) = 2

Concept used:
P = A/[1 + (R/100)]ⁿ
Interest = 2 × Installment – P

Calculation:
Let the loan amount be P.
P = 5808/[1 + (10/100)] + 5808/[1 + (10/100)]²
⇒ P = 5808/(1 + 1/10) + 5808/(1 + 1/10)²
⇒ P = 5808/(11/10) + 5808/(11/10)²
⇒ P = (5808 × 10)/11 + 5808/(121/100)
⇒ P = 58080/11 + 580800/121
⇒ P = 5280 + 4800
⇒ P = 10080
Interest = 2 × 5808 – 10080
⇒ 11616 – 10080
⇒ 1536
∴ The total interest charged in this scheme is Rs. 1,536.