Consider the compound interest in the following cases:
(A) The compound interest on Rs 16000 at 20% per annum for 9 months, compounded quarterly is Rs. 2500
(B) The compound interest on Rs 2800 at 10% per annum for 18 months is Rs. 434.
Choose the correct statement(s):
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → Only (B)
Under compound interest, the interest of each period is added to the principal, and the next period’s interest is worked out on the new amount. The compound interest is the final amount minus the principal.
(A) The compound interest on Rs 16000 at 20% per annum for 9 months, compounded quarterly is Rs. 2500 Incorrect.
Compounded quarterly, the rate is \(20\div4=5\%\) a quarter and 9 months are 3 quarters, so the interest is Rs 2522, not Rs 2500:
After the 1st quarter: \(16000\times1.05=16800\)
After the 2nd quarter: \(16800\times1.05=17640\)
After the 3rd quarter: \(17640\times1.05=18522\)
Compound interest \(=18522-16000=\) Rs 2522
(B) The compound interest on Rs 2800 at 10% per annum for 18 months is Rs. 434. Correct.
No period is stated, so the interest is compounded yearly, the usual rule; for the half year left over, half the yearly rate is charged on the amount after one year.
After 1 year: \(2800\times1.10=3080\)
Interest for the next 6 months at 5%: \(3080\times\frac{5}{100}=154\)
So the amount is \(3080+154=3234\)
Compound interest \(=3234-2800=\) Rs 434