CAT 2021 Slot 3 · Quant · Question 21

CAT 2021 Slot 3 previous year question on Simple Interest and Compound Interest, with the answer and a step-by-step solution.

Simple Interest and Compound InterestArithmeticMultiple choiceMedium
Bank A offers 6% interest rate per annum compounded half yearly. Bank B and Bank C offer simple interest but the annual interest rate offered by Bank C is twice that of Bank B. Raju invests a certain amount in Bank B for a certain period and Rupa invests ₹10,000 in Bank C for twice that period. The interest that would accrue to Raju during that period is equal to the interest that would have accrued had he invested the same amount in Bank A for one year. The interest accrued, in ₹, to Rupa is
  1. A
    2436
  2. B
    3436
  3. C
    2346
  4. D
    1436
Pick an option, then check.
Answer & solution

Answer: Option A

Bank A pays 3\% per half year, twice a year, so one year multiplies the amount by {\left( 1.03 \right)}^{2}=1.0609: an effective 6.09\%.

Let Raju invest P in Bank B at rate r for time t, earning simple interest Prt. We are told this equals what Bank A would have given in one year, namely 0.0609P.

So Prt=0.0609P, giving rt=0.0609. Note that P cancels and is never needed.

Rupa invests 10000 in Bank C at rate 2r for time 2t, so her interest is 10000\times \left( 2r \right)\times \left( 2t \right)=10000\times 4rt.

That is 10000\times 4\times 0.0609=2436, so Rupa earns ₹2436.

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