Question

In what time will a sum of rs 3750 at 20% per annum compounded annually amount to rs 6480?

Answer 1

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Answer 2

Answer:

$\red { Time } \green {= 3\: years }$

Step-by-step explanation:

$Principal (P) = Rs\:3750$

$Rate \:of \: interest (r) = 20\% \: per \:annum$

$Amount (A) = Rs\:6480$

$Let \: number \:of \:times \: interest \:paid = n$

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

$\implies 6480 = 3750\left( 1 + \frac{20}{100}\right)^{n}$

$\implies \frac{6480}{3750} = \left( 1 + \frac{1}{5}\right)^{n}$

$\implies \frac{216}{125} = \left( \frac{6}{5}\right)^{n}$

$\implies \left(\frac{6}{5}\right)^{3} = \left( \frac{6}{5}\right)^{n}$

$\implies 3 = n$

$\boxed { \orange { If \: a^{m} = a^{n} \: then \:m = n }}$

Therefore.,

$\red { Time } \green {= 3\: years}$

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