Simple interest on a certain sum at 8% per annum for 5 years is ₹2400. What will be the compound interest on the same sum at the same rate for 2 years?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → ₹998.40
The simple interest gives the principal; compound interest for 2 years is then the amount after 2 years minus the principal.
The principal, from \(\text{SI}=\frac{P\times R\times T}{100}\):
SI for 5 years at 8%: \(\displaystyle 2400=\frac{P\times8\times5}{100}\)
Principal \(P=6000\)
The compound interest for 2 years at 8%:
Amount \(=6000\times(1.08)^{2}=6000\times1.1664=6998.40\)
CI \(=6998.40-6000=998.40\)
Shortcut: For 2 years, compound interest is the simple interest plus interest on the first year’s interest; the principal is not needed.
SI for one year \(=2400\div5=480\), so SI for 2 years \(=960\)
Interest on 480 at 8% \(=38.40\)
CI \(=960+38.40=998.40\)