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Question : What is the compound interest on INR 10000 in 1 year 6 months at 10% per annum, the interest being compounded half-yearly?

Option 1: INR 1625.50

Option 2: INR 1576.25

Option 3: INR 1826.50

Option 4: INR 1422.25


Team Careers360 25th Jan, 2024
Answer (1)
Team Careers360 27th Jan, 2024

Correct Answer: INR 1576.25


Solution : Rate, $R$ = 10%
Term, $n$ = 1 year
Principal sum, $P$ = INR 10000
When compounded half-yearly,
Amount = $P(1+\frac{R}{200})^{2n}$
Compound interest = $P(1+\frac{R}{200})^{2n}-P$
= $10000(1+\frac{10}{200})^{2×1.5}-10000$
= $10000(1+\frac{1}{20})^{3}-10000$
= $10000(\frac{21}{20})^{3}-10000$
= $10000(\frac{21^3}{20^3}-1)$
= $10000(\frac{21^3-20^3}{8000})$
= $\frac{10000×(441+400+420)×1}{8000}$
= $\frac{12610}{8}$
= INR $1576.25$
Hence, the correct answer is INR 1576.25.

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