Simple Interest Capital Recovery

CAT 2022 Slot 2 · QA · Easy · Arithmetic

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Mr. Pinto invests one-fifth of his capital at 6%, one-third at 10% and the remaining at 1%, each rate being simple interest per annum. Then, the minimum number of years required for the cumulative interest income from these investments to equal or exceed his initial capital is

Answer

20

Explanation

Let total capital be CC. Investments: 15C\frac{1}{5} C at 6%6\% SI 13C\frac{1}{3} C at 10%10\% SI Remaining fraction = 1−15−13=715C1 - \frac{1}{5} - \frac{1}{3} = \frac{7}{15} C at 1%1\% SI. Annual interest earned = (15×6%+13×10%+715×1%)C\left(\frac{1}{5} \times 6\% + \frac{1}{3} \times 10\% + \frac{7}{15} \times 1\%\right) C =(1.2100+10300+71500)C=(18+50+71500)C=751500C=120C=5%C= \left(\frac{1.2}{100} + \frac{10}{300} + \frac{7}{1500}\right) C = \left(\frac{18 + 50 + 7}{1500}\right) C = \frac{75}{1500} C = \frac{1}{20} C = 5\% C. To accumulate interest equal to CC, time required T=C120C=20T = \frac{C}{\frac{1}{20} C} = 20 years.

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