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Compound interest principal calculation

CAT 2020 Slot 3 · Quantitative Ability · Easy · SI & CI

This is an easy Quantitative Ability question from the CAT 2020 Slot 3 paper. It tests SI & CI. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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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

16000

Explanation

Interest rate per half-year r=10/2=5%r = 10 / 2 = 5\%. Time t=1.5 years=3t = 1.5\text{ years} = 3 half-years.

Amount A=P(1+5100)3=P(2120)3=18522A = P \left(1 + \frac{5}{100}\right)^3 = P \left(\frac{21}{20}\right)^3 = 18522. P×92618000=18522  ⟹  P=2×8000=16000P \times \frac{9261}{8000} = 18522 \implies P = 2 \times 8000 = 16000.

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