Question

4. In how many years will Rs. 1500 amount to Rs 2592 if it is
invested in 20% p.a. interest, interest being compounded
annually?

Answer 1

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

Given that,

Rs. 1500 amount to Rs 2592 if it is invested at the 20% p.a., interest being compounded annually.

Let assume that the time period be n years.

So we have,

↝ Sum invested, p = Rs 1500

↝ Amount, A = Rs 2592

↝ Rate of interest, r = 20 % per annum compounded annually.

↝ Time period = n years

We know,

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

$\red{\rm :\longmapsto\:\boxed{ \tt{ \: Amount = p {\bigg[1 + \dfrac{r}{100} \bigg]}^{n} \: }}}$

So, On substituting the values, we get

$\rm :\longmapsto\:2592 = 1500 {\bigg[1 + \dfrac{20}{100} \bigg]}^{n}$

$\rm :\longmapsto\:1296 = 750{\bigg[1 + \dfrac{1}{5} \bigg]}^{n}$

$\rm :\longmapsto\:648 = 375{\bigg[ \dfrac{5 + 1}{5} \bigg]}^{n}$

$\rm :\longmapsto\:216 = 125{\bigg[ \dfrac{6}{5} \bigg]}^{n}$

$\rm :\longmapsto\: {\bigg[ \dfrac{6}{5} \bigg]}^{n} = \dfrac{216}{125}$

$\rm :\longmapsto\: {\bigg[ \dfrac{6}{5} \bigg]}^{n} = \dfrac{6 \times 6 \times 6}{5 \times 5 \times 5}$

$\rm :\longmapsto\: {\bigg[ \dfrac{6}{5} \bigg]}^{n} = {\bigg[\dfrac{6}{5} \bigg]}^{3}$

$\red{\bf\implies \:\boxed{ \tt{ \: n \: = \: 3 \: }}}$

So, it took 3 years for Rs. 1500 amount to Rs 2592 if it is

invested in 20% p.a., interest being compounded annually.

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Explore more :-

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

$\red{\rm :\longmapsto\:\boxed{ \tt{ \: Amount = p {\bigg[1 + \dfrac{r}{200} \bigg]}^{2n} \: }}}$

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

$\red{\rm :\longmapsto\:\boxed{ \tt{ \: Amount = p {\bigg[1 + \dfrac{r}{400} \bigg]}^{4n} \: }}}$

3. Amount on a certain sum of money of Rs p invested at the rate of r % per annum compounded monthly for n years is

$\red{\rm :\longmapsto\:\boxed{ \tt{ \: Amount = p {\bigg[1 + \dfrac{r}{1200} \bigg]}^{12n} \: }}}$