Question

A sum of Rs. 1275 is borrowed at 4% pa compound interest and paid back in 2 equal annual installments. What is the amount of each installment?

1. Rs. 676
2. Rs. 700
3. Rs. 650
4. Rs. 500
5. Rs. 850

Answer 1

Correct Answer - Option 1 : Rs. 676

Given:

The principal is Rs. 1275

Rate of interest is 4 %

Number of installment is 2.

Formula used:

P( 1+ R/100)ⁿ = X( 1+ R/100)^n-1  +  X( 1+ R/100)^n-2  + X( 1+ R/100)^{n -3} +  X( 1+ R/100)^n-4 + ----

Where,

P = principal

R = Rate       

n = number of installments

X = amount of installment

Calculation:

Let the value of installment be Rs. X

⇒ 1275(1 + 4/100)² = X(1 + 4/100)^2-1

⇒ 1275 × 104/100 × 104/100 = (X + 104 X/100)

⇒ 1275 × 104/100 × 104/100 = 204 X/100

⇒ X = 676

∴ The value of installment is Rs. 676.