CAT 2020 Slot 2 QA Question 25: For the same principal amount, the compound interest for two years at 5% per annum exceeds the simple interest for three years at 3% per annum by ₹ 1125. Then the principal amount in rupees is

Question

For the same principal amount, the compound interest for two years at 5% per annum exceeds the simple interest for three years at 3% per annum by ₹ 1125. Then the principal amount in rupees is

Accepted Answer

Let the principal be $P$.

Compound interest for two years at 5% is
$P \left((1.05)^2 - 1ight)$
$= 0.1025P$

Simple interest for three years at 3% is
$P 	imes 3 	imes \dfrac{3}{100}$
$= 0.09P$

Their difference is ₹1125.
$0.1025P - 0.09P = 1125$
$0.0125P = 1125$
$P = 90000$

Answer: 90000