Question

find the principal which amounts to 2704 years at 4% per annum, compounded annually ​

Answer 1

Appropriate Question :-

Find the principal which amounts to 2704 in 1 year at 4% per annum, compounded annually.

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

Given that,

Amount on a certain sum of money = 2704

Rate of interest, r = 4 % per annum compounded annually

Time, n = 1 year

Let assume that, Principal be P

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 given by

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

So, on substituting the values of Amount, r and n, we get

$\rm \: 2704 \: = \: P \: {\bigg[1 + \dfrac{4}{100} \bigg]}^{1}$

$\rm \: 2704 \: = \: P \: {\bigg[1 + \dfrac{1}{25} \bigg]}$

$\rm \: 2704 \: = \: P \: {\bigg[ \dfrac{25 + 1}{25} \bigg]}$

$\rm \: 2704 \: = \: P \: {\bigg[ \dfrac{26}{25} \bigg]}$

$\rm \: P = \dfrac{2704 \times 25}{26}$

$\rm \: P = 104 \times 25$

$\bf\implies \:P \: = \: 2600$

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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 given by

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

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 given by

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

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 given by

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