Question

a sum of 10000 yields 3310 as compound interest in 3 year's. if interest is compounded yearly, find the amount and rate of interest​

Answer 1

$Given \: Principal (P) = Rs \: 10000,\\Compound \: Interest (C.I) = Rs \: 3310 ,\\Time (T) = 3 \: years$

/* As Interest is compounded yearly , so there will be 3 conversation periods */

$n = 3$

$Let \: Amount = A \: and \\Rate \: of \: Interest = r$

$\boxed {\pink { A = P + C.I }}$

$= Rs \: 10000 + Rs \: 3310 \\= Rs \: 13310$

$\boxed { \orange { A = P\left( 1+ \frac{r}{100}\right)^{n} }}$

$\implies 13310 = 10000\left ( 1 + \frac{r}{100}\right)^{3}$

$\implies \frac{13310}{10000} = \left( 1 + \frac{r}{100}\right)^{3}$

$\implies \frac{1331}{1000} = \left( 1 + \frac{r}{100}\right)^{3}$

$\implies \big(\frac{11}{10}\big)^{3}= \left( 1 + \frac{r}{100}\right)^{3}$

$\implies \frac{11}{10}= 1 + \frac{r}{100}$

$\implies \frac{11}{10} - 1 = \frac{r}{100}$

$\implies \frac{11-10}{10} = \frac{r}{100}$

$\implies \frac{1}{10} = \frac{r}{100}$

$\implies \frac{100}{10} = r$

$\implies r = 10\%$

Therefore.,

$\red { Amount (A) }\green { = Rs \:13310 }$

$\red{ Rate \:of \: Interest }\green {= 10\%}$

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