Question

What total amount is to be paid on a sum of Rs. 12,000 for \(1 \frac{1}{2}\) years at 10% per annum compounded half yearly?
1. Rs. 13,891.50
2. Rs. 19,831.50
3. Rs. 31,918.50
4. Rs. 13,230.50

Answer 1

Correct Answer - Option 1 : Rs. 13,891.50

Given:

The sum = Rs 12,000

Time = \(1 \frac{1}{2}\) years

Rate = 10% p.a.

Formula used:

A = P(1 + R/100)^t

Here, A, P, R and t are the Amount, Principal, Rate and time respectively

Concept used:

When compounded half-yearly then,

Rate is half and time is doubled

Calculation:

Rate = 10%/2 = 5% and Time = \(1 \frac{1}{2}\) × 2 = 3 half yearly

Now, A = P(1 + R/100)t

⇒ A = 12000(1 + 5/100)³

⇒ A = 12000 × 21/20 × 21/20 × 21/20

⇒ A = 13891.5

∴ The total amounts to be paid is Rs 13891.50