Question

A person borrows Rs. 3,200 to be paid back with compound interest at the rate of 5% per annum by the end of 2 years in two equal yearly instalments. Then each instalment (in rupees) is
1. 1,721
2. 1,880
3. 1,894
4. 1,924

Answer 1

Correct Answer - Option 1 : 1,721

Given:

The amount borrowed is Rs. 3,200

Rate is 5% per annum

Time is 2 years

Formula used:

A = P{1 + (R/100)}^T

Where, 

A is Amount

P is Principal

R is Rate

And, T is Time

Calculations:

Let each installment be Rs. x

According to the question, we have

A = P{1 + (R/100)}T

P = A/{1 + (R/100)}T

⇒ 3,200 = x/{1 + (5/100)}¹ + x/{1 + (5/100)}2

⇒ 3,200 = x/(21/20) + x/(441/400)

⇒ 3,200 = 20x/21 + 400x/441

⇒ 3,200 = (420x + 400x)/441

⇒ 3,200 = 820x/441

⇒ x = (3,200 × 441)/820

⇒ x = 1,720.97

⇒ x = Rs. 1,721

∴ The amount of each installment is Rs. 1,721.