What will be the difference in the compound interest if a sum of Rs.12,000 is compounded annually and half-yearly at an annual rate of 10% for 2 years?
Note: Round off the decimal to the nearest number.
Show answer & explanation
Correct answer: C
Explanation
The correct answer is Option 3 i.e. Rs.66.
A = P(1 + R/100)T
where, A = Amount, P = Principal, R = Rate and T = time
When compounded annually
⇒ A = 12000(1 + 10/100)2
⇒ A = 12000(1 + 1/10)2
⇒ A = 12000 × 11/10 × 11/10
⇒ A = 14520
C.I. = Amount - Principal = 14520 - 12000 = Rs. 2520
When compounded half-yearly
R = 10/2 = 5% and T = 4 years
⇒ A = 12000(1 + 5/100)4
⇒ A = 12000(1 + 1/20)4
⇒ A = 12000 × 21/20 × 21/20 × 21/20 × 21/20
⇒ A = 14586.075
C.I. = Amount - Principal = 14586.075 - 12000 = Rs. 2586.075
Difference = 2586.075 - 2520 = Rs.66.075 or Rs.66