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CAT 2020 Slot 2 — QA Question 18

Simple and Compound InterestEasy

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 Rs 1125. Then the principal amount in rupees is

Answer & solution

Answer: 90000

Solution

Easy

Write both interests as decimal multiples of the principal PP: simple interest is linear, compound interest uses the growth factor squared. Set their difference equal to Rs 11251125 and solve for PP.

1

Simple interest, 3 years at 3%.

SI=P×3100×3=0.09 P\begin{aligned} &\text{SI} = P\times \tfrac{3}{100}\times 3 = 0.09\,P \end{aligned}
2

Compound interest, 2 years at 5%.

CI=P(1.05)2−P=P(1.1025−1)=0.1025 P\begin{aligned} &\text{CI} = P(1.05)^2 - P = P(1.1025 - 1) = 0.1025\,P \end{aligned}
3

Apply the difference and solve.

0.1025 P−0.09 P=1125⇒ 0.0125 P=1125⇒ P=11250.0125=90000\begin{aligned} &0.1025\,P - 0.09\,P = 1125\\ &\Rightarrow\ 0.0125\,P = 1125\\ &\Rightarrow\ P = \frac{1125}{0.0125} = 90000 \end{aligned}
Principal=Rs 90000\text{Principal} = \text{Rs }90000
CAT 2020 Slot 2 QA Q18: For the same principal amount, the compound interest for two years at 5% per annum exceeds the simple interest — Solution | TheCATExam