Question

Mr. Hiralal invested Rs 215000 in a mutual fund he got Rs 305000 after two years. Mr. Ramniklal invested Rs 140000 at 8 % compound interest for 2 years in a bank. find out the percentage gain of each of them. Whose investment was more profitable.

Answer 1

Hint: We are given the investment amount of both Hiralal and Ramniklal. Returns Hiralal got from mutual funds are also given. We can get the total gain by Hiralal as the difference between the returns and investment. Then we can find the percentage gain given by the relation $p.g=\dfrac{g}{i}\times 100\%$, where p.g is percentage gain; g is gain and i is the investment. It is given that Ramniklal is getting a compound interest of 8% for 2 years. We can find the future value of compound interest given by the relation $FV={{\left( 1+\dfrac{r}{100} \right)}^{n}}P$, where FV is the future value, P is present value of investment, r is the rate of interest in percentage and n is the number of compounding periods. Once we get the future value, we can get the gain as the difference of future value and present value. Percentage gain can be found from the above relation.

Complete step by step answer:
It is given that Hiralal invested Rs 215000 and he got Rs 305000 after two years from mutual funds.
Therefore, his gain will be given as the difference of the returns and investment.
$\Rightarrow $ g = 305000 – 215000
$\Rightarrow $ g = Rs 90000
The percentage gain is given by the relation $p.g=\dfrac{g}{i}\times 100\%$, where p.g is percentage gain; g is gain and i is the investment.
Therefore, we will substitute g = Rs 90000 and i = 215000
$\begin{align}
  & \Rightarrow p.{{g}_{Hiralal}}=\dfrac{90000}{215000}\times 100\% \\
 & \Rightarrow p.{{g}_{Hiralal}}=0.4186\times 100\% \\
 & \Rightarrow p.{{g}_{Hiralal}}=41.86\% \\
\end{align}$
Therefore, the percentage gain of Hiralal is 41.86 %.
Now, it is given that Ramniklal invested Rs 140000 in a bank at 8 % compound interest. To find the total gain, we need to find the future value of the investment given by the relation $FV={{\left( 1+\dfrac{r}{100} \right)}^{n}}P$, where FV is the future value, P is present value of investment, r is the rate of interest in percentage and n is the number of compounding periods.
Thus, we will substitute r = 8, n = 2 and P = 140000 in the given relation find the value of FV.
$\begin{align}
  & \Rightarrow FV={{\left( 1+\dfrac{8}{100} \right)}^{2}}\left( 140000 \right) \\
 & \Rightarrow FV={{\left( 1+0.08 \right)}^{2}}\left( 140000 \right) \\
 & \Rightarrow FV={{\left( 1.08 \right)}^{2}}\left( 140000 \right) \\
 & \Rightarrow FV=\left( 1.1664 \right)\left( 140000 \right) \\
 & \Rightarrow FV=163296 \\
\end{align}$
Therefore, after two years, Ramniklal will get a return of Rs 163296. Thus, total gain will be difference of return and investment.
$\Rightarrow $ g = 163296 – 140000
$\Rightarrow $ g = Rs 23296
The percentage gain can be calculated by the relation $p.g=\dfrac{g}{i}\times 100\%$.
$\begin{align}
  & \Rightarrow p.{{g}_{Ramniklal}}=\dfrac{23296}{140000}\times 100\% \\
 & \Rightarrow p.{{g}_{Ramniklal}}=0.1664\times 100\% \\
 & \Rightarrow p.{{g}_{Ramniklal}}=16.64\% \\
\end{align}$
Therefore, percentage gain by Ramniklal is 16.64 %.

Hence, we can see that percentage gain of Hiralal is more than that of Ramniklal.

Note: This problem is an example of interest and percentage. Thus, students are advised to be well versed with concepts of compound interest as it may seem complicated in the beginning. Students may confuse between SI and CI.