Question

What sum of money will amount to Rs.$5,445\,in\,2\,years\,at\,10\% $ per annum compound interest?

Answer 1

Hint: Compound interest is in the interest to principal sum of a loan or deposit, or in other words, interest on interest. It is the result of interest, rather than paying it so that interest in the next period is then earned on the principal sum plus previously accumulated interest.
Compound interest formula can be given as, $A = P{\left( {1 + \dfrac{r}{{100}}} \right)^T}$

Where,${\text{A}} = $Total Amount, ${\text{P}} = $Principal amount, ${\text{r}} = $Rate of interest & ${\text{T}} = $Time period

Complete step by step solution:
Let sum of money be $'P'$
Given, $Amount\, = \,A\, = \,Rs.\,5445$
$Time\,period\, = \,T = \,2 years$
$Rate\,of\,\,interest\, = \,R\, = \,10\%$
We know that formula of compound interest is,

$A = P{\left( {1 + \dfrac{R}{{100}}} \right)^T} \\

\Rightarrow 5445 = P{\left( {1 + \dfrac{{1{0}}}{{10{0}}}} \right)^2} \\
\Rightarrow5445 = P{\left( {1 + \dfrac{1}{{10}}} \right)^2} \\
\Rightarrow5445 = P{\left( {\dfrac{{10 + 1}}{{10}}} \right)^2} \\
\Rightarrow5445 = P{\left( {\dfrac{{11}}{{10}}} \right)^2} \\
\Rightarrow5445 = P\left( {\dfrac{{121}}{{100}}} \right) \\
P = \dfrac{{{{5445}} \times 100}}{{{{121}}}}\, = \,45 \times 100 \\
P = 4500 \\$

Hence, the sum of money $ = Rs.\,4500$.

Note: We know that formula of compound interest play an important role to solve such types of problems. Time period should be written in the form of years not months. We need to avoid any type of calculation mistakes.
Compound interest can also be calculated by using formula of simple interest $I = \dfrac{{P \times R \times T}}{{100}}$ by adding interest of previous in principle in a commutative manner.