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CAT 2024 Slot 2 — QA Question 20

Simple and Compound InterestEasy

Anil invests Rs 22000 for 6 years in a scheme with 4% interest per annum, compounded half-yearly. Separately, Sunil invests a certain amount in the same scheme for 5 years, and then reinvests the entire amount he receives 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 equal, then the initial investment, in rupees, made by Sunil is

Answer & solution

  • 20808

  • B

    20860

  • C

    20480

  • D

    20640

Solution

Medium

Anil's amount is a clean compound-interest growth at 2% per half-year for 12 periods. Sunil grows for 10 half-year periods then 1 year of 10% simple interest. Set the two final amounts equal and solve for Sunil's principal.

1

Anil's amount after 6 years. 4% per annum compounded half-yearly =2%=2\% per half-year, 6×2=126\times2=12 periods.

AAnil=22000 (1.02)12\begin{aligned} &A_{\text{Anil}}=22000\,(1.02)^{12} \end{aligned}
2

Sunil's amount after 6 years. Principal PP grows for 5 years =10=10 periods at 2%, then 1 year at 10% simple interest (×1.10\times1.10).

ASunil=P (1.02)10×1.10\begin{aligned} &A_{\text{Sunil}}=P\,(1.02)^{10}\times 1.10 \end{aligned}
3

Equate and solve. Set ASunil=AAnilA_{\text{Sunil}}=A_{\text{Anil}}; the factor (1.02)10(1.02)^{10} cancels.

P (1.02)10×1.10=22000 (1.02)12⇒ P=22000 (1.02)21.10(cancel (1.02)10)⇒ P=22000×1.04041.10=22888.81.10=20808\begin{aligned} &P\,(1.02)^{10}\times1.10=22000\,(1.02)^{12}\\ &\Rightarrow\ P=\frac{22000\,(1.02)^{2}}{1.10} \quad\text{(cancel }(1.02)^{10}\text{)}\\ &\Rightarrow\ P=\frac{22000\times1.0404}{1.10}=\frac{22888.8}{1.10}=20808 \end{aligned}
Sunil’s investment=Rs 20808\text{Sunil's investment}=\text{Rs }20808
CAT 2024 Slot 2 QA Q20: Anil invests Rs 22000 for 6 years in a scheme with 4% interest per annum, compounded half-yearly. Separately, — Solution | TheCATExam