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CAT 2019 Slot 2 — QA Question 32

Simple and Compound InterestEasy

Amal invests Rs 12000 at 8% interest, compounded annually, and Rs 10000 at 6% interest, compounded semi-annually, both investments being for one year. Bimal invests his money at 7.5% simple interest for one year. If Amal and Bimal get the same amount of interest, then the amount, in Rupees, invested by Bimal is

Answer & solution

Correct answer: 20920

Answer: 20920

Solution

Easy

Compute Amal's total interest from his two compound deposits (annual on the first, semi-annual on the second), then equate it to Bimal's simple interest at 7.5%7.5\% for one year to find Bimal's principal.

1

Amal — first deposit (8%8\% annual).

I1=12000×0.08=960\begin{aligned} &I_1 = 12000\times 0.08 = 960 \end{aligned}
2

Amal — second deposit (6%6\% semi-annual). Two half-years at 3%3\% each.

A2=10000 (1.03)2=10609⇒ I2=10609−10000=609\begin{aligned} &A_2 = 10000\,(1.03)^2 = 10609\\ &\Rightarrow\ I_2 = 10609 - 10000 = 609 \end{aligned}
3

Total interest of Amal.

I=I1+I2=960+609=1569\begin{aligned} &I = I_1 + I_2 = 960 + 609 = 1569 \end{aligned}
4

Match Bimal's simple interest. Let Bimal invest XX at 7.5%7.5\% for one year.

X×0.075=1569(equal interest)⇒ X=15690.075=20920\begin{aligned} &X\times 0.075 = 1569 \quad\text{(equal interest)}\\ &\Rightarrow\ X = \frac{1569}{0.075} = 20920 \end{aligned}
Bimal invests Rs. 20920\text{Bimal invests Rs. }20920

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CAT 2019 Slot 2 QA Q32: Amal invests Rs 12000 at 8% interest, compounded annually, and Rs 10000 at 6% interest, compounded semi-annual — Solution | TheCATExam