[tex]\large\underline{\sf{Solution-}}[/tex]
Given that,
A sum of money becomes ₹ 26,471 at an interest rate of 3% per annum compounded annually after a period of one year.
So we have
Amount = ₹ 26471
Rate of interest, r = 3 % per annum compounded annually.
Time, n = 1 year
Let assume that sum invested be ₹ P.
We know,
Amount received on a certain sum of money of ₹ P invested at the rate of r % per annum compounded annually for n years is given by
[tex]\boxed{ \rm{ \:Amount \: = \: P \: {\bigg[1 + \dfrac{r}{100} \bigg]}^{n} \: \: }} \\ [/tex]
So, on substituting the values, we get
[tex]\rm \: 26471 = P {\bigg[1 + \dfrac{3}{100} \bigg]}^{1} \\ [/tex]
[tex]\rm \: 26471 = P {\bigg[\dfrac{100 + 3}{100} \bigg]}^{1} \\ [/tex]
[tex]\rm \: 26471 = P {\bigg[\dfrac{103}{100} \bigg]}^{} \\ [/tex]
[tex]\rm \: P = 26471 \times {\bigg[\dfrac{100}{103} \bigg]}^{} \\ [/tex]
[tex]\rm\implies \:P \: = \: 25700 \\ [/tex]
Hence,
₹ 25700 becomes ₹ 26,471 at an interest rate of 3% per annum compounded annually after a period of one year.
[tex]\rule{190pt}{2pt}[/tex]
Additional Information :-
1. Amount received on a certain sum of money of ₹ P invested at the rate of r % per annum compounded semi - annually for n years is given by
[tex]\boxed{ \rm{ \:Amount \: = \: P \: {\bigg[1 + \dfrac{r}{200} \bigg]}^{2n} \: \: }} \\ [/tex]
2. Amount received on a certain sum of money of ₹ P invested at the rate of r % per annum compounded quarterly for n years is given by
[tex]\boxed{ \rm{ \:Amount \: = \: P \: {\bigg[1 + \dfrac{r}{400} \bigg]}^{4n} \: \: }} \\ [/tex]
3. Amount received on a certain sum of money of ₹ P invested at the rate of r % per annum compounded monthly for n years is given by
[tex]\boxed{ \rm{ \:Amount \: = \: P \: {\bigg[1 + \dfrac{r}{1200} \bigg]}^{12n} \: \: }} \\ [/tex]
[tex]p \times (1 + \frac{r}{100} )^{t} [/tex]
[tex]p(1 + \frac{3}{100} )^{1} = 26471[/tex]
[tex]p \times \frac{103}{100} = 26471[/tex]
[tex]p = 25700[/tex]
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Verified answer
[tex]\large\underline{\sf{Solution-}}[/tex]
Given that,
A sum of money becomes ₹ 26,471 at an interest rate of 3% per annum compounded annually after a period of one year.
So we have
Amount = ₹ 26471
Rate of interest, r = 3 % per annum compounded annually.
Time, n = 1 year
Let assume that sum invested be ₹ P.
We know,
Amount received on a certain sum of money of ₹ P invested at the rate of r % per annum compounded annually for n years is given by
[tex]\boxed{ \rm{ \:Amount \: = \: P \: {\bigg[1 + \dfrac{r}{100} \bigg]}^{n} \: \: }} \\ [/tex]
So, on substituting the values, we get
[tex]\rm \: 26471 = P {\bigg[1 + \dfrac{3}{100} \bigg]}^{1} \\ [/tex]
[tex]\rm \: 26471 = P {\bigg[\dfrac{100 + 3}{100} \bigg]}^{1} \\ [/tex]
[tex]\rm \: 26471 = P {\bigg[\dfrac{103}{100} \bigg]}^{} \\ [/tex]
[tex]\rm \: P = 26471 \times {\bigg[\dfrac{100}{103} \bigg]}^{} \\ [/tex]
[tex]\rm\implies \:P \: = \: 25700 \\ [/tex]
Hence,
₹ 25700 becomes ₹ 26,471 at an interest rate of 3% per annum compounded annually after a period of one year.
[tex]\rule{190pt}{2pt}[/tex]
Additional Information :-
1. Amount received on a certain sum of money of ₹ P invested at the rate of r % per annum compounded semi - annually for n years is given by
[tex]\boxed{ \rm{ \:Amount \: = \: P \: {\bigg[1 + \dfrac{r}{200} \bigg]}^{2n} \: \: }} \\ [/tex]
2. Amount received on a certain sum of money of ₹ P invested at the rate of r % per annum compounded quarterly for n years is given by
[tex]\boxed{ \rm{ \:Amount \: = \: P \: {\bigg[1 + \dfrac{r}{400} \bigg]}^{4n} \: \: }} \\ [/tex]
3. Amount received on a certain sum of money of ₹ P invested at the rate of r % per annum compounded monthly for n years is given by
[tex]\boxed{ \rm{ \:Amount \: = \: P \: {\bigg[1 + \dfrac{r}{1200} \bigg]}^{12n} \: \: }} \\ [/tex]
SOLUTION —>
GIVEN:A sum of money becomes ₹26,471 at an interest rate of 3% per annum compounded annually after a period of 1 year. Find the sum.
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AMOUNT=₹26,471
RATE = 3%(LET'S TAKE RATE AS r)
Time=1 year
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Formula used=>
[tex]p \times (1 + \frac{r}{100} )^{t} [/tex]
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LET'S DO
[tex]p(1 + \frac{3}{100} )^{1} = 26471[/tex]
[tex]p \times \frac{103}{100} = 26471[/tex]
[tex]p = 25700[/tex]
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ADDITIONAL INFORMATION
The amount can be calculated half-yearly. When the amount is calculated half-yearly the rate becomes half.
The amount can be calculated quarterly. When the amount is calculated quarterly the rate becomes 1/4 .