Question

Find the amount to be paid at the end of 6 months on Rs.1800 at 8% per annum compounded quarterly.

Answer 1

Hint: In order to solve this problem, we need to understand compound interest. Compound interest is interest calculated on the initial principal which also includes all the accumulated interest from the previous periods.
The formula for compound interest is $A=P{{\left( 1+\dfrac{r}{100} \right)}^{n}}$ where A = amount of previous value, P = principal value, n = number of years, r = the rate of interest.

Complete step-by-step answer:
Let’s first understand what compound interest is.
Compound interest is interest calculated on the initial principal which also includes all the accumulated interest from the previous periods.
The formula for compound interest is $A=P{{\left( 1+\dfrac{r}{100} \right)}^{n}}$ where A = amount of previous value, P = principal value, n = number of years, r = the rate of interest.
According to the question the values given are,
Principal amount = Rs.1800.
Rate of interest = 8% quarterly
Therefore, the rate of interest quarterly is $8\times \dfrac{1}{4}=2\%$ .
We are asked after 6 months but by converting into years we are asked the amount after $\dfrac{6}{12}=\dfrac{1}{2}$ years.
As the interest is added 4 times a year the time period for this calculation is $4\times \dfrac{1}{2}=2$ quarterly years.
Therefore, n = 2
Substituting all the values we get,
$A=1800{{\left( 1+\dfrac{2}{100} \right)}^{2}}$
Solving the equation, we get,
$\begin{align}
  & A=1800\times {{\left( 1.02 \right)}^{2}} \\
 & =1872.72 \\
\end{align}$
Hence, the amount to be paid after 6 months is Rs. 1872.72.

Note: We need to understand that as the interest is calculated quarterly we need to change the rate of interest and time period accordingly in terms of quarterly hours. For the rate of interest, we need to dive by 4 and for the time period, we need to multiply the number of years by 4. The principal amount does not affect yearly or quarterly interest. So it does not change whatsoever.