Question

In how many years will Rs. 200000 amount to Rs. 266200 at 10% compound interest?​

Answer 1

$\large\underline{\sf{Solution-}}$

Given that

Principal, P = Rs 200000

Amount, A = Rs 266200

Rate of interest, r = 10 % per annum compounded annually.

Let assume that, Time taken be 'n' years.

We know that,

Amount (A) on a certain sum of money of Rs P invested at the rate of r % per annum compounded annually for n years is

$\boxed{ \bf{ \: A = P {\bigg[1 + \dfrac{r}{100} \bigg]}^{n}}}$

where,

A is amount

P is Principal

r is rate of interest per annum

n is time period

So, on substituting the values, we get

$\rm :\longmapsto\:266200 = 200000 {\bigg[1 + \dfrac{10}{100} \bigg]}^{3}$

$\rm :\longmapsto\:2662 \cancel{00} = 2000\cancel{00} {\bigg[1 + \dfrac{1}{10} \bigg]}^{3}$

$\rm :\longmapsto\:2662 = 2000 {\bigg[\dfrac{10 + 1}{10} \bigg]}^{n}$

$\rm :\longmapsto\:\dfrac{2662}{2000} = {\bigg[\dfrac{11}{10} \bigg]}^{n}$

$\rm :\longmapsto\:\dfrac{1331}{1000} = {\bigg[\dfrac{11}{10} \bigg]}^{n}$

$\rm :\longmapsto\:\dfrac{11 \times 11 \times 11}{10 \times 10 \times 10} = {\bigg[\dfrac{11}{10} \bigg]}^{n}$

$\rm :\longmapsto\:\bigg[\dfrac{11}{10 } \bigg] ^{3} = {\bigg[\dfrac{11}{10} \bigg]}^{n}$

$\bf\implies \:n \: = \: 3$

Hence,

In 3 years will Rs. 200000 amount to Rs. 266200 at 10% compound interest.

Additional Information :-

1. Amount (A) on a certain sum of money of Rs P invested at the rate of r % per annum compounded semi - annually for n years is

$\boxed{ \bf{ \: A = P {\bigg[1 + \dfrac{r}{200} \bigg]}^{2n}}}$

2. Amount (A) on a certain sum of money of Rs P invested at the rate of r % per annum compounded quarterly for n years is

$\boxed{ \bf{ \: A = P {\bigg[1 + \dfrac{r}{400} \bigg]}^{4n}}}$