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
1. Rs. 13,891.50
2. Rs. 19,831.50
3. Rs. 31,918.50
4. Rs. 13,230.50
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