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CAT 2021 Slot 1 — QA Question 20

Compound InterestEasy

Anil invests some money at a fixed rate of interest, compounded annually. If the interests accrued during the second and third year are ₹ 806.25 and ₹ 866.72, respectively, the interest accrued, in INR, during the fourth year is nearest to

Answer & solution

  • A

    934.65

  • B

    926.84

  • 931.72

  • D

    929.48

Solution

Easy

In annual compound interest, each year's interest is the previous year's interest multiplied by the growth factor (1+r100)\left(1+\tfrac{r}{100}\right). So consecutive yearly interests form a geometric progression. Find the common ratio from years 2 and 3, then extend one more year.

1

Interest grows geometrically. Let the growth factor be k=1+r100k=1+\tfrac{r}{100}. Then each year's interest is kk times the previous year's.

I3=k⋅I2⇒ k=I3I2=866.72806.25\begin{aligned} &I_3=k\cdot I_2\\ &\Rightarrow\ k=\frac{I_3}{I_2}=\frac{866.72}{806.25} \end{aligned}
2

Compute the growth factor.

k=866.72806.25=1.075(so r=7.5%)\begin{aligned} &k=\frac{866.72}{806.25}=1.075\quad\text{(so }r=7.5\%) \end{aligned}
3

Extend to the fourth year. The fourth-year interest is kk times the third-year interest.

I4=k⋅I3=1.075×866.72⇒ I4=931.72 (nearest)\begin{aligned} &I_4=k\cdot I_3=1.075\times 866.72\\ &\Rightarrow\ I_4=931.72\ (\text{nearest}) \end{aligned}
≈INR 931.72 (option c)\approx \text{INR }931.72\ \text{(option c)}

You never need the principal or rr explicitly: I4=I3 2I2=866.722806.25≈931.72I_4=\dfrac{I_3^{\,2}}{I_2}=\dfrac{866.72^2}{806.25}\approx 931.72, since the interests form a GP.

CAT 2021 Slot 1 QA Q20: Anil invests some money at a fixed rate of interest, compounded annually. If the interests accrued during the — Solution | TheCATExam