Question

A loan is to be returned in two equal annual instalments. If the rate of interest is 10% p. a., compounded yearly, and each instalment is Rs. 3,872, then the total interest charged in this instalment scheme is:
1. Rs. 1,024
2. Rs. 1,020
3. Rs. 980
4. Rs. 1,050

Answer 1

Correct Answer - Option 1 : Rs. 1,024

Given:

Rate of interest, R = 10%

Annual installment, x = Rs. 3872

Total number of installments, N = 2

Formula used:

P = [x/(1 + R/100)] + [x/(1 + R/100)²] +.....+ [x/(1 + R/100)ⁿ]

where,

P = Principal borrowed 

x = Annual Installments

R = Rate of Interest

Calculation:

Since, Total number of installments is 2.

Value of 2 installments = 2 × Rs. 3872

⇒ Value of 2 installments = Rs. 7744

Now,

P = [x/(1 + R/100)] + [x/(1 + R/100)2]

⇒ P = [3872/(1 + 10/100)] + [3872/(1 + 10/100)²]

⇒ P = [3872/(11/10)] + [3872/(11/10)²]

⇒ P = [(3872 × 10)/11] + [(3872 × 100)/121]

⇒ P = 3520 + 3200

⇒ P = Rs. 6720

Total interest charged = Value of 2 installments - Principal borrowed

⇒ Total interest charged = Rs. 7744 - Rs. 6720

⇒ Total interest charged = Rs. 1024

∴ The total interest charged in this installment scheme is Rs. 1024.