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CAT 2021 Slot 3 — QA Question 14

Simple and Compound InterestEasy

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 INR, to Rupa is

Answer & solution

  • A

    2346

  • B

    3436

  • C

    1436

  • 2436

Solution

Easy

Set up Raju's simple interest in Bank B and equate it to one year's compound interest in Bank A (at 6%6\% p.a. compounded half-yearly =3%=3\% per half-year). This pins down the product rtrt. Rupa's interest in Bank C uses double the rate and double the time, so it reduces to a multiple of that same rtrt.

1

Name the variables. Let Raju invest amount AA in Bank B at r%r\% p.a. for tt years. Then Rupa invests ₹10000\mathbf{₹}10000 in Bank C at 2r%2r\% p.a. for 2t2t years (rate doubled, time doubled).

Raju’s interest=A⋅r⋅t100\begin{aligned} &\text{Raju's interest} = \frac{A\cdot r\cdot t}{100} \end{aligned}
2

One year in Bank A. 6%6\% compounded half-yearly means 3%3\% for each of 22 periods.

Amount=A(1+3100)2=1.0609 A⇒ Interest=1.0609A−A=0.0609 A\begin{aligned} &\text{Amount} = A\left(1+\tfrac{3}{100}\right)^2 = 1.0609\,A\\ &\Rightarrow\ \text{Interest} = 1.0609A - A = 0.0609\,A \end{aligned}
3

Equate to get rtrt. Raju's Bank B interest equals this Bank A interest.

A r t100=0.0609 A(given equality)⇒ r t=6.09\begin{aligned} &\frac{A\,r\,t}{100} = 0.0609\,A \quad\text{(given equality)}\\ &\Rightarrow\ r\,t = 6.09 \end{aligned}
4

Rupa's interest. Simple interest on ₹10000₹10000 at 2r%2r\% for 2t2t years.

Interest=10000⋅2r⋅2t100=400 (rt)⇒ Interest=400×6.09=2436\begin{aligned} &\text{Interest} = \frac{10000\cdot 2r\cdot 2t}{100} = 400\,(rt)\\ &\Rightarrow\ \text{Interest} = 400\times 6.09 = 2436 \end{aligned}
₹ 2436₹\,2436
CAT 2021 Slot 3 QA Q14: Bank A offers 6% interest rate per annum compounded half yearly. Bank B and Bank C offer simple interest but t — Solution | TheCATExam