Question

. A sum of money deposited at compound interest amounts to Birr 8820 in two years and Birr 9261 in 3 years find the rate of interest compounded annually
A) 6% B) 1 0.5% C) 4.5% D) 5% E) 1 0%

Answer 1

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

Let us assume that

• Sum deposited = Rs p

• Rate of interest = r % per annum compounded annually.

We know that,

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

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

So, According to statement

A sum of money deposited at compound interest amounts to Birr 8820 in two years.

$\rm :\longmapsto\:8820 = p {\bigg[1 + \dfrac{r}{100} \bigg]}^{2} - - - (1)$

According to second condition

A sum of money deposited at compound interest amounts to Birr 9261 in three years

$\rm :\longmapsto\:9261 = p {\bigg[1 + \dfrac{r}{100} \bigg]}^{3} - - - (2)$

On dividing equation (2) by equation (1), we get

$\rm :\longmapsto\:\dfrac{9261}{8820} = \dfrac{p {\bigg[1 + \dfrac{r}{100} \bigg]}^{3} }{p {\bigg[1 + \dfrac{r}{100} \bigg]}^{2}}$

$\rm :\longmapsto\:\dfrac{441}{420} = 1 + \dfrac{r}{100}$

$\rm :\longmapsto\:\dfrac{21}{20} = 1 + \dfrac{r}{100}$

$\rm :\longmapsto\:\dfrac{21}{20} - 1 = \dfrac{r}{100}$

$\rm :\longmapsto\:\dfrac{21 - 20}{20} = \dfrac{r}{100}$

$\rm :\longmapsto\:\dfrac{1}{20} = \dfrac{r}{100}$

$\bf\implies \:r \: = \: 5 \: \%$

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Additional Information :-

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

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

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

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

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

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

Answer 2

Given:

A sum of money deposited at compound interest amounts to Birr 8820 in two years and Birr 9261 in 3 years

Find:

Find the rate of interest compounded annually.

Let us assume that

Sum deposited = Rs p

Rate of interest = r % per annum compounded annually.

We know that,

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

$Amount=p[1+\frac{r}{100} ]^{n}$

So, According to a statement

A sum of money deposited at compound interest amounts to Birr 8820 in two years.

$8820=p[1+\frac{r}{100} ]^{2}----1)$

According to the second condition

A sum of money deposited at compound interest amounts to Birr 9261 in three years

$9261=p[1+\frac{r}{100} ]^{3}----2)$

On dividing equation (2) by equation (1), we get

$\frac{9261}{8820} =\frac{p[1+\frac{r}{100} ]^{3}}{p[1+\frac{r}{100} ]^{2}}$

$\frac{441}{420}=1+\frac{r}{100}$

$\frac{21}{20}=1+\frac{r}{100}$

$\frac{21}{20}-1=\frac{r}{100}$

$\frac{21-20}{20}=\frac{r}{100}$

$\frac{1}{20}=\frac{r}{100}$

$r=5%$%