Question

If the amount after 3 years at the rate of$12\dfrac{1}{2}\%$per annum compounded annually is \[Rs.10,935\], find the principal?

Answer 1

Hint: Type of question is based on the profit, interest and compound interest. As in question we are asked to find out the principal, and compound interest is given. So we can directly apply the formula of compound i.e. $C~=~P{{\left. \left( 1~+~\dfrac{r}{n} \right. \right)}^{nt}}$in which ‘C’ is the compound Interest, ‘P’ is the principal amount, r is the rate of interest kept in the ratio form not in percent form, ‘n’ is number of times interest applied per time period and ‘t’ is the number of time period elapsed. So according to the question we have all the information asked in the compound in the compound interest formula except the principal value, which we need to find. So we will put the value we have in the compound interest formula from where we can easily get the principal value.

Complete step by step answer:
So moving ahead with the question we have, Total Amount compounded annually after 3 years is equal to\[Rs.10,935\]. Which is calculated after the time elapsed of 3 years at the rate of interest of $12\dfrac{1}{2}\%$which is interest applied annually per time period. So now putting all these value in the formula we will get;
\[\begin{align}
  & C~=~P{{\left. \left( 1~+~\dfrac{r}{n} \right. \right)}^{nt}} \\
 & 10935~=~P{{\left. \left( 1~+~\dfrac{25}{2\times 100}\times \dfrac{1}{1} \right. \right)}^{1\times 3}} \\
 & 10935~=~P{{\left. \left( 1~+~\dfrac{25}{200} \right. \right)}^{3}} \\
 & 10935~=~P{{\left. \left( 1~+~\dfrac{1}{8} \right. \right)}^{3}} \\
 & 10935~=~P{{\left. \left( ~\dfrac{9}{8} \right. \right)}^{3}} \\
 & p=\dfrac{10935\times 8\times 8\times 8}{9\times 9\times 9} \\
 & p=7,680 \\
\end{align}\]
Hence principal amount is \[Rs.7,680\]

Note: While using the compound interest formula, keep in mind that we had to put the rate of interest in terms of ratio, rather than writing it in percent form, to convert percent form into ratio divide it by 100, as we did it in our case.