Question

Find the amount and the compound interest on $Rs. 2500$ for $2 years$ at $10%$ per annum compounded annually.

Answer 1

Hint: The first part we need to find is the amount generated compounding for \[2\text{ }years\] at \[10%\] per annum and after that we need to find the compound interest by subtracting the principal from the amount.
To find the amount we use the formula:
\[A=P{{\left( 1+\dfrac{R}{100} \right)}^{T}}\]
To find the compound interest we use the formula:
\[C.I.=A-P\]
where \[C.I.,A,P,T\] and \[R\] is compound interest, amount, principal, time (in years) and rate percentage respectively.

Complete step-by-step answer:
Now we put the values in the formula to find amount, \[P=Rs.2500\], \[T=2years\], \[R=10%\] as:
\[A=P{{\left( 1+\dfrac{R}{100} \right)}^{T}}\]
\[A=2500{{\left( 1+\dfrac{10}{100} \right)}^{2}}\]
\[A=2500\left( 1+\dfrac{10}{100} \right)\left( 1+\dfrac{10}{100} \right)\]
\[A=2500\left( \dfrac{110}{100} \right)\left( \dfrac{110}{100} \right)\]
\[A=2500\times 1.21\]
\[A=Rs.\text{ }3025\]
Now to find the compound interest we subtract the principal from the amount:
\[C.I.=A-P\]
\[C.I.=Rs.\text{ }3025-Rs.\text{ 2500}\]
\[C.I.=Rs.\text{ 525}\]
Hence, the Amount \[=Rs.\text{ }3025\] and Compound Interest \[=Rs.\text{ 525}\].

Note: Another method to find the amount and the compound interest is to first find the compound interest and then add it to the principal to find the amount. To find the compound interest first we use the formula as \[C.I.=P\left[ {{\left( 1+\dfrac{R}{100} \right)}^{T}}-1 \right]\] and then after finding the compound interest we add the interest to find the amount as [\A=C.I+P\].