What is the difference between the compound interest (in Rs) compounded yearly and compounded Half Yearly for 18 months at 20% per annum on a sum of Rs 12,000?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 132
Principal = Rs. 12000
Time = 18 months
Rate of interest = 20%
Simple interest = (Principal × Time × Rate)/100
Compound interest = Amount - Principal
A = P × (1 + r/100)t
When interest is compounded yearly -
At the end of the first year, the principal = 12000 × 1.21 = Rs. 14400
Then, after 6 months the interest accumulated on the principal amount of Rs. 14400 = (14400 × 20 × 6/12)/100 = 1440
After 8 months the initial principal amount becomes = 14400 + 1440 = Rs. 15840
Interest accumulated in 18 months = Rs. (15840 - 12000) = Rs. 3840
When interest compounded half-yearly -
Rate of interest (R) = 20/2 % = 10%
Time (n) = 18/6 = 3
Principal = 12,000
After 18 months the principal becomes = 12000(1 + 10/100)3 = Rs. 15972
Interest accumulated in 18 months = Rs. (15972 - 12000) = Rs. 3972
The difference between the interest accumulated = Rs. (3972 - 3840) = Rs. 132