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Investment interest comparison

CAT 2019 Slot 2 · Quantitative Ability · Medium · Simple interest & Compound interest

This is a medium Quantitative Ability question from the CAT 2019 Slot 2 paper. It tests Simple interest & Compound interest. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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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

[TITA]

Answer

20920

Explanation

Interest on Amal's first investment =12000×0.08=960= 12000 \times 0.08 = 960 Rs.

Interest on Amal's second investment (6% compounded semi-annually =3%= 3\% per half year): 10000×[(1.03)2−1]=10000×0.0609=609 Rs10000 \times \left[(1.03)^2 - 1\right] = 10000 \times 0.0609 = 609\text{ Rs}

Total interest earned by Amal =960+609=1569= 960 + 609 = 1569 Rs.

Let PP be the amount invested by Bimal at 7.5% SI: P×0.075=1569  ⟹  P=15690.075=20920 RsP \times 0.075 = 1569 \implies P = \frac{1569}{0.075} = 20920\text{ Rs}

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