Consider the compound interest of the following
(A) The compound interest on Rs 16000 at 20% per annum for 9 months, compounded quarterly is: Rs 2522
(B) The compound interest on Rs 2800 at 10% per annum for 18 months, compounded annually is: Rs 434
Choose the correct statement(s):
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → Both (A) and (B)
In compound interest the interest is added to the principal at the end of every conversion period, and the next period’s interest is worked out on the new amount. For a period shorter than a year, the yearly rate is divided in proportion to the period, and a part-year left over at the end earns simple interest for that part.
(A) The compound interest on Rs 16000 at 20% per annum for 9 months, compounded quarterly is: Rs 2522 Correct.
Rate per quarter \(=\frac{20}{4}=5\%\); 9 months \(=3\) quarters
Amount \(=16000\times1.05^3=16000\times1.157625=18522\)
CI \(=18522-16000=2522\)
(B) The compound interest on Rs 2800 at 10% per annum for 18 months, compounded annually is: Rs 434 Correct.
After the first year: \(2800\times1.10=3080\)
The last 6 months earn half a year’s interest, 5%, on 3080: \(3080\times0.05=154\)
Amount \(=3080+154=3234\)
CI \(=3234-2800=434\)