The compound interest (in Rs.) on a sum of Rs. 12,000 at 10% per annum for 1.5 years, interest compounded half-yearly, is:
1. Rs. 1,750
2. Rs. 1,900
3. Rs. 1,821.50
4. Rs. 1,891.50
1. Rs. 1,750
2. Rs. 1,900
3. Rs. 1,821.50
4. Rs. 1,891.50
Correct Answer – Option 4 : Rs. 1,891.50
Given:
A sum = Rs. 12,000
Rate = 10% per annum
And time = 1.5 years.
Formula used:
Amount = Principal{1 + (R/100)}n
Where n = time in years and R = rate percentage/annum
Compund interest = Amount – Principal
If time = n years, rate = R% and interest compounded half-yearly
Then time = 2n and rate = (R/2)%
Calculation:
Interest compounded half-yearly:
Then time = 2 × 1.5
⇒ 3 years
And the rate = 10/2
⇒ 5%
Amount = 12000 × {1 + (5/100)}3
⇒ 12000 × {1 + (1/20)}3
⇒ 12000 × {(20 + 1)/20}3
⇒ 12000 × (21/20)3
⇒ 12000 × (9261/8000)
⇒ 12 × 9261/8
⇒ 1,11,132/8
⇒ Rs. 13891.5
Compound interest = amount – principal
⇒ 13891.5 – 12000
⇒ Rs. 1891.5
∴ The compound interest is Rs. 1891.5