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At what rate per cent per annum will Rs 32000 yield a compound interest of Rs 5044 in 9 months interest being compounded quarterly ? |
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Answer» Principal = Rs 32000 Amount = Rs (32000 + 5044) = Rs 37044 Rate = r% p.a. or \(\frac{r}{4}\)% per quarter Time = 9 months = 3 quarters, i.e., n = 3 \(\therefore\) Applying A= P\(\big(1+\frac{r}{100}\big)^n\) , we have 37044 = 32000\(\big(1+\frac{r}{400}\big)^3\) \(\Rightarrow\) \(\frac{37044}{32000}\) = \(\big(1+\frac{r}{400}\big)^3\) \(\Rightarrow\) \(\frac{9261}{8000}\) = \(\big(1+\frac{r}{400}\big)^3\) \(\Rightarrow\) \(\big(\frac{21}{20}\big)^3\) = \(\big(1+\frac{r}{400}\big)^3\) \(\Rightarrow\) 1 + \(\frac{r}{400}\) = \(\frac{21}{20}\) \(\Rightarrow\) \(\frac{r}{100}\) = \(\frac{21}{20}\)-1 = \(\frac{1}{20}\) \(\Rightarrow\) r = \(\frac{400}{20}\) = 20% p.a |
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