What will be the compound interest of Rs 16000 for 9 months at 20% per annum if compounded quarterly?

Correct Answer:

Description for Correct answer:

Principal= Rs. 16000,Rate %=20 %Time= 9 months When interest is being compounded quaterlyTime=\( \Large \frac{9}{12} \times 4=3 \) Rate =\( \Large \frac{20}{4} \%=5 \%=\frac{1}{20} \)

According to the question, 8000 units = Rs. 16000 1 unit = Rs. 2 1261 units = Rs.\( \Large 2 \times 1261\)

= Rs. 2522

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Q. The compound interest on 16000 Rs. for 9 months at 20% per annum, interest being compounded quarterly, is:
Answer: [C] Rs. 2522
Notes: The interest is compounded quarterly, $ \therefore R = \frac{20}{4} = 5\%$ Time = 3 quarters $ \therefore C.I. = P\left [ \left ( 1+\frac{R}{100} \right )^{T} – 1 \right ]$ $ = 16000\left [ \left ( 1+\frac{5}{100} \right )^{3} – 1 \right ]$ $ = 16000\left [ \left ( \frac{21}{20} \right )^{3} – 1 \right ]$ $ = 16000\left ( \frac{9261 – 8000}{8000} \right )$ $ = 16000\times \frac{1261}{8000} = 2522 Rs.$ Hence option [C] is correct answer.

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The compound interest on a certain sum of money at 21% for 2 years is ₹9,282. Its simple interest (in ₹) at the same rate and for the same period is:

Answer & Explanation Answer: B) 8,400

Explanation:

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₹4,000 is given at 5% per annum for one year and interest is compounded half yearly. ₹2,000 is given at 40% per annum compounded quarterly for 1 year. The total interest received is nearest to:

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Explanation:

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Q:

A sum amounts to ₹18,600 after 3 years and to ₹27,900 after 6 years, at a certain rate percent p.a., when the interest is compounded annually. The sum is:

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Explanation:

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The compound interest on ₹ 16000 for 9 months at 20% p.a, compounded quarterly is ₹ 2522

True

Explanation;

Hint:

Principal (P) = 16000

n = 9 months = `9/12` years

r = 20% p.a

For compounding quarterly, we have to use below formula,

Amount (A) = `"P" xx (1 + "r"/100)^(4"n")`

Since quarterly we have to divide ‘r’ by 4

r = `20/4` = 5%

A = `1600(1 + 5/100)^(9/12 xx 4)`

= `16000(105/100)^(9/12 xx 4)`

= `16000(105/100)^(9/3)`

= `16000 xx (21/20)^3`

= `16000 xx 21/20 xx 21/20 xx 21/20`

= 18522

∴ Interest A – P = 18522 – 16000 = 2522

Concept: Concept of Compound Interest

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