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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% D) 21%

 A) 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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