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The compound interest on a sum of RS. 4000 becomes RS. 630.50 in 9 months. Find the rate of interest, if interest is compounded quarterly.
|
A) 20% |
|
B) 23% |
|
C) 19% |
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D) 21% |
Correct Answer:
| A) 20% |
Description for Correct answer:
Given, P = RS. 4000, n = 9 months = \( \Large \frac{3}{4}yr \)
and CI= RS. 630.
Amount = P + CI = 4000 + 630.50 = rs. 4630.50
According to the formula,
Amount = \( \Large P \left(1+ \frac{R}{100\times 4}\right)^{4n} \)
=> 4630.50=\( \Large 4000 \left(1+ \frac{R}{400}\right)^{4\times 3/4} \)
=> 4630.50=\( \Large 4000 \left(\frac{400+R}{400}\right)^{3} \)
=> \( \Large \frac{4630.50}{4000} \)=\( \Large \left(\frac{400+R}{400}\right)^{3} \)
=> \( \Large \frac{9261}{8000} \)=\( \Large \left(\frac{400+R}{400}\right)^{3} \)
=> \( \Large \left(\frac{21}{20}\right)^{3} \)=\( \Large \left(\frac{400+R}{400}\right)^{3} \)
=> \( \Large \frac{400+R}{400} \)=\( \Large \frac{21}{20} \)
=> 400+R=\( \Large 21\times 20 \)=420
R=420-400=20%
Given, P = RS. 4000, n = 9 months = \( \Large \frac{3}{4}yr \)
and CI= RS. 630.
Amount = P + CI = 4000 + 630.50 = rs. 4630.50
According to the formula,
Amount = \( \Large P \left(1+ \frac{R}{100\times 4}\right)^{4n} \)
=> 4630.50=\( \Large 4000 \left(1+ \frac{R}{400}\right)^{4\times 3/4} \)
=> 4630.50=\( \Large 4000 \left(\frac{400+R}{400}\right)^{3} \)
=> \( \Large \frac{4630.50}{4000} \)=\( \Large \left(\frac{400+R}{400}\right)^{3} \)
=> \( \Large \frac{9261}{8000} \)=\( \Large \left(\frac{400+R}{400}\right)^{3} \)
=> \( \Large \left(\frac{21}{20}\right)^{3} \)=\( \Large \left(\frac{400+R}{400}\right)^{3} \)
=> \( \Large \frac{400+R}{400} \)=\( \Large \frac{21}{20} \)
=> 400+R=\( \Large 21\times 20 \)=420
R=420-400=20%
Part of solved Compound interest questions and answers : >> Aptitude >> Compound interest
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