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Compound and Simple Interest Comparison

CAT 2023 Slot 1 · Quantitative Ability · Medium · Arithmetic

This is a medium Quantitative Ability question from the CAT 2023 Slot 1 paper. It tests Arithmetic. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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Anil invests Rs. 22000 for 6 years in a certain scheme with 4% interest per annum, compounded half-yearly. Sunil invests in the same scheme for 5 years, and then reinvests the entire amount received at the end of 5 years for one year at 10% simple interest. If the amounts received by both at the end of 6 years are same, then the initial investment made by Sunil, in rupees, is

Answer

20808

Explanation

Interest rate per half-year =4%2=2%= \frac{4\%}{2} = 2\%.

For Anil (6 years =12= 12 half-years): AmountA=22000×(1.02)12\text{Amount}_A = 22000 \times (1.02)^{12}

For Sunil (5 years =10= 10 half-years, then 1 year at 10% SI): Let initial investment be PP. Amount after 5 years=P×(1.02)10\text{Amount after 5 years} = P \times (1.02)^{10} AmountS=P×(1.02)10×(1+0.10)=P×(1.02)10×1.10\text{Amount}_S = P \times (1.02)^{10} \times (1 + 0.10) = P \times (1.02)^{10} \times 1.10

Equating both amounts: 22000×(1.02)12=P×(1.02)10×1.1022000 \times (1.02)^{12} = P \times (1.02)^{10} \times 1.10 22000×(1.02)2=P×1.1022000 \times (1.02)^2 = P \times 1.10 22000×1.0404=1.10P22000 \times 1.0404 = 1.10 P P=20000×1.0404=20808P = 20000 \times 1.0404 = 20808

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