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CAT 2020 Slot 3 — QA Question 20

Compound InterestEasy

A person invested a certain amount of money at 10% annual interest, compounded half-yearly. After one and a half years, the interest and principal together became Rs 18522. The amount, in rupees, that the person had invested is

Answer & solution

Answer: 16000

Solution

Medium

Compounding is half-yearly, so the rate per period is half the annual rate and 1.51.5 years is 33 periods. Write the amount formula and solve for the principal, using the convenient cube (2120)3\left(\tfrac{21}{20}\right)^3.

1

Per-period rate and number of periods. Annual rate 10%10\% compounded half-yearly.

rate per half-year=5%,periods=1.5 yr0.5 yr=3\begin{aligned} &\text{rate per half-year}=5\%,\qquad \text{periods}=\frac{1.5\ \text{yr}}{0.5\ \text{yr}}=3 \end{aligned}
2

Amount equation. With principal PP.

P(1+5100)3=18522⇒ P(2120)3=18522\begin{aligned} &P\left(1+\frac{5}{100}\right)^{3}=18522\\ &\Rightarrow\ P\left(\frac{21}{20}\right)^{3}=18522 \end{aligned}
3

Solve for PP. Note 213=926121^3=9261 and 18522=2×926118522=2\times 9261.

P×213203=18522⇒ P=18522×203213=2×9261×80009261⇒ P=2×8000=16000\begin{aligned} &P\times\frac{21^{3}}{20^{3}}=18522\\ &\Rightarrow\ P=18522\times\frac{20^{3}}{21^{3}}=2\times 9261\times\frac{8000}{9261}\\ &\Rightarrow\ P=2\times 8000=16000 \end{aligned}
P=Rs 16000P=\text{Rs }16000
CAT 2020 Slot 3 QA Q20: A person invested a certain amount of money at 10% annual interest, compounded half-yearly. After one and a ha — Solution | TheCATExam