Question

in how many years rupees 1000 ammount to 1464.10 rupees. if the rate of intrest is 10% p.a compounded annually.​

Answer 1

$principal (p) = 1000 \\ rate \: of \: interest(r) = 10\% \\ amount(a) = 1464.10 \\ \\ a = p {(1 + \frac{r}{100} )}^{n} \\ 1464.10 = 1000 {(1 + \frac{10}{100}) }^{n} \\ 1464.10 = 1000 {( \frac{100 + 10}{100} )}^{n} \\ 1464.10 = 1000 {( \frac{110}{100} )}^{n} \\ \frac{1464.10}{1000} = { (\frac{110}{100} )}^{n} \\ \frac{14641}{10000} = {( \frac{110}{100} )}^{n} \\ {( \frac{11}{10}) }^{4} = {( \frac{11}{10}) }^{n} \\ 4 = n \: \: \: (if \: bases \: are \: same \: then \: powers \: will \: be \: equal)$

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