Question

What sum of money will accumulate to Rs. 5300 at 8% rate of interest in 9 months?

Answer 1

Hint: In this particular question use the concept that the compound interest is calculated as, \[C.I.=A-P\], where P = principal amount and A= amount after compound interest. So, A is calculated as \[A=P{{\left( 1+\dfrac{r}{100} \right)}^{n}}\], where r is the rate of interest in percentage, n is the time in years. So, use these concepts to reach the solution of the equation.

Complete step-by-step solution:
According to the question it is asked to find the principal amount if the total finest amount is 5300 at 8% rate of interest in 9 months.
Given data: Total amount = 5300
Rate of interest = 8%
Time in months \[=9=\dfrac{9}{12}\] years
Now, we know that the total amount ‘A’ is calculated as, \[A=P{{\left( 1+\dfrac{r}{100} \right)}^{n}}\]
And we know that Amount = Principal + interest
The equation is given as,
Principal + Principal \[\times \] interest rate \[\times \] time period = Amount
\[\begin{align}
  & x+x\times R\times T=5300 \\
 & x+x\times 8\%\times \dfrac{9}{12}=5300 \\
\end{align}\]
After solving this,
\[\begin{align}
  & 53x=265000 \\
 & x=5000 \\
\end{align}\]
Hence, the sum of money is Rs. 5300.

Note:Whenever we face such types of questions the key concept we have to remember is the formula of compound interest which is stated above. So, first change the given compounded monthly to compounded yearly then convert to fraction in integer by multiplying it by 12 and divide the interest by the same number. So, overall no change will occur.