Consider the compound interest of the following
(A) The compound interest on Rs 30500 at 15% per annum for 2 years. (compounded annually) is: Rs. 9836.25
(B) The compound interest of Rs 5000 at 20% per annum for one year is compounded (half-yearly) is: Rs. 6050.
Which of the following statements is/are correct?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → Only (A)
Under compound interest, amount \(=P\left(1+\frac{R}{100}\right)^n\), where \(n\) is the number of conversion periods, and compound interest \(=\) amount \(-\) principal. When interest is compounded half-yearly, the rate per period is halved and the number of periods doubled.
(A) The compound interest on Rs 30500 at 15% per annum for 2 years. (compounded annually) is: Rs. 9836.25 Correct.
2 yearly periods at 15%: amount \(=30500\times(1.15)^2=30500\times1.3225=40336.25\)
Taking away the principal, CI \(=40336.25-30500=9836.25\), as stated
(B) The compound interest of Rs 5000 at 20% per annum for one year is compounded (half-yearly) is: Rs. 6050. Incorrect. Rs 6050 is the amount, not the interest:
Rate per half-year \(=10\%\); periods in one year \(=2\)
2 periods at 10%: amount \(=5000\times(1.1)^2=5000\times1.21=6050\)
Taking away the principal, CI \(=6050-5000=1050\)