Question

find the rate percent per annum if rupees 25000 amount to rupees 26010 in 6 months interest is compounded quarterly​

Answer 1

Answer:

$\red { Rate } \green { = 8\% }$

Step-by-step explanation:

$Principal (P) = Rs\: 25000$

$Amount (A) = Rs\:26010$

$Let \: rate \: of \: interest \:for \\ 3 \: months =\frac{r}{4} \%$

$As \: interest \: is \: compounded \: quarterly, \\So\: there \: will \: be \: 2 \: conversion \: periods\\in \: 6 \: months$

$n = 2$

$\boxed { \pink { A = P\left( 1+\frac{ \frac{r}{4}}{100}\right)^{n}}}$

$\implies 26010 = 25000\left( 1+\frac{ \frac{r}{4}}{100}\right)^{2}$

$\implies \frac{26010}{25000} = \left( 1+\frac{ r}{400}\right)^{2}$

$\implies \left( \frac{51}{50}\right)^{2} = \left( 1+\frac{ r}{400}\right)^{2}$

$\implies \frac{51}{50} = 1+ \frac{r}{400}$

$\implies \frac{51}{50} -1 = \frac{r}{400}$

$\implies \frac{51-50}{50} = \frac{r}{400}$

$\implies \frac{1}{50} = \frac{r}{400}$

$\implies\frac{1}{50} \times 400 = r$

$\implies 8 = r$

Therefore.,

$\red { Rate } \green { = 8\% }$

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