Question

How much will Rs. 25,000 amount to in 2 years at com- pound interest, if the rates for the successive years be 4 and 5 per cent per year?


pls answer the above question correctly​

Answer 1

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

Given that,

Rs. 25,000 invested for 2 years at compound interest, if the rates for the successive years be 4 and 5 per cent per year.

So, we have

Principal, P = Rs 25000

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

Time, n = 1 year

Rate of interest, R = 5 % per annum compounded annually

Time, m = 1 year

We know,

Amount received on a certain sum of money of Rs P invested at the rate of r % per annum compounded annually for n years and R % per annum compounded annually for next m years is given by

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

So, on substituting the values, we get

$\rm \: Amount = 25000 {\bigg[1 + \dfrac{4}{100} \bigg]}^{1} {\bigg[1 + \dfrac{5}{100} \bigg]}^{1}$

$\rm \: Amount = 25000 {\bigg[1 + \dfrac{1}{25} \bigg]} {\bigg[1 + \dfrac{1}{20} \bigg]}$

$\rm \: Amount = 25000 {\bigg[ \dfrac{25 + 1}{25} \bigg]} {\bigg[ \dfrac{20 + 1}{20} \bigg]}$

$\rm \: Amount = 25000 {\bigg[ \dfrac{26}{25} \bigg]} {\bigg[ \dfrac{21}{20} \bigg]}$

$\rm\implies \:Amount = Rs \: 27300$

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

Additional Information :-

1. Amount received 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

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

2. Amount received 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

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

3. Amount received 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

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

4. Amount received 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

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

Answer 2

Answer:

Given :-

• A sum of Rs 25000 amount in 2 years at compound interest, if the rate for the successive years be 4% and 5% per per year.

To Find :-

• What is the amount.

Formula Used :-

$\clubsuit$ Amount Formula :

$\bigstar \: \: \sf\boxed{\bold{\pink{A =\: P\bigg\lgroup 1 + \dfrac{r_1}{100}\bigg\rgroup \bigg\lgroup 1 + \dfrac{r_2}{100}\bigg\rgroup}}}\: \: \: \bigstar$

where,

• A = Amount
• P = Principal
• r₁ = Rate of interest for the first year
• r₂ = Rate of interest for the second year

Solution :-

Given :

• Principal = Rs 25000
• Rate of Interest (r₁) = 4% per annum
• Rate of Interest (r₂) = 5% per annum
• Time = 2 years

According to the question by using the formula we get,

$\implies \sf A =\: 25000\bigg\lgroup 1 + \dfrac{4}{100}\bigg\rgroup \bigg\lgroup 1 + \dfrac{5}{100}\bigg\rgroup$

$\implies \sf A =\: 25000\bigg\lgroup \dfrac{100 + 4}{100}\bigg\rgroup \bigg\lgroup \dfrac{100 + 5}{100}\bigg\rgroup$

$\implies \sf A =\: 25000\bigg\lgroup \dfrac{104}{100}\bigg\rgroup \bigg\lgroup \dfrac{105}{100}\bigg\rgroup$

$\implies \sf A =\: 25000 \times \dfrac{104}{100} \times \dfrac{105}{100}$

$\implies \sf A =\: \dfrac{25000 \times 104 \times 105}{10000}$

$\implies \sf A =\: \dfrac{27300\cancel{0000}}{1\cancel{0000}}$

$\implies \sf A =\: \dfrac{27300}{1}$

$\implies \sf\bold{\red{A =\: Rs\: 27300}}$

$\therefore$ The amount is Rs 27300 .