Question

Find the value that Rs 1000 would amount to under compound interest at 20% p.a, interest being compounded annually in 3 years.
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Answer 1

Answer:

A = P(1 + R/100)n

A = 1000× 120/100 × 120/100 × 120/100

A = 1728

Compound interest = 1728 - 1000

Compound interest =728

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Answer 2

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

Sum invested, p = Rs 1000

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

Time, n = 3 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

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

So, on substituting the values, we get

$\rm :\longmapsto\:{ \tt{ \: Amount \: = \: 1000 \: {\bigg[1 + \dfrac{20}{100} \bigg]}^{3} \: }}$

$\rm :\longmapsto\:{ \tt{ \: Amount \: = \: 1000 \: {\bigg[1 + \dfrac{1}{5} \bigg]}^{3} \: }}$

$\rm :\longmapsto\:{ \tt{ \: Amount \: = \: 1000 \: {\bigg[\dfrac{5 + 1}{5} \bigg]}^{3} \: }}$

$\rm :\longmapsto\:{ \tt{ \: Amount \: = \: 1000 \: {\bigg[\dfrac{6}{5} \bigg]}^{3} \: }}$

$\rm :\longmapsto\:{ \tt{ \: Amount \: = \: 1000 \: \times \dfrac{216}{125} }}$

$\rm :\longmapsto\:{ \tt{ \: Amount \: = \: 216 \times 8}}$

$\rm :\longmapsto\:{ \tt{ \: Amount \: = \:1728}}$

So,

The value that Rs 1000 would amount to under compound interest at 20% p.a, interest compounded annually in 3 years = Rs 1728

More to know :-

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

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

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

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

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

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