Question

Mr. Hiralal invested $Rs.215000$ in a mutual fund. He got $Rs.305000$ after $2$ 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: The given problem is related to percentages and compound interest. Try to recall the formulae related to percentage change and compound interest. Find the amount received by Mr. Ramniklal after two years using the concept of compound interest. Then, calculate the percentage gain in the case of Mr. Hiralal and Mr. Ramniklal using the formula of the percentage change. Then compare them.
Complete step-by-step answer:
Before proceeding with the solution, first, we will understand the formulae used in the solution of the problem.
The first formula is for finding the percentage change.
If ${{V}_{i}}$ and ${{V}_{f}}$ are the initial and final values of an entity respectively, then the percentage change in the value of the entity is given as $\%change=\dfrac{{{V}_{f}}-{{V}_{i}}}{{{V}_{i}}}\times 100\%$ .
The second formula is for calculation of the final amount in the case of compound interest.
The formula for compound interest is given as $A=P{{\left( 1+\dfrac{r}{100} \right)}^{n}}$ , where $A=$ Amount after $n$ compounding, $P=$ principal amount, $r=$ rate of interest, $n=$ number of times the interest is compounded in the given time.
If $T$ is the total time for which interest is to be calculated, then:
i) $n=T$ , if the interest is compounded annually.
ii) $n=2T$ , if the interest is compounded half-yearly
iii) $n=4T$ , if the interest is compounded quarterly.
Now, we will consider the case of Mr. Hiralal. It is given that Mr. Hiralal invested $Rs.215000$ in a mutual fund and got $Rs.305000$ after $2$ years.
Now, let $H$ be the percentage gain for Mr. Hiralal.
So, the percentage gain for Mr. Hiralal is given as $H=\dfrac{305000-215000}{215000}\times 100%$ .
$=\dfrac{90000}{215000}\times 100\%$
$=0.4186\times 100\%$
$=41.86\%$
So, $H=41.86\%$ .
Now, let’s consider the case of Mr. Ramniklal. It is given that he invested $Rs.140000$ at $8\%$ compound interest for $2$ years in a bank. So, $P=140000,r=8\%$ and $n=2$.
So, the amount received by Mr. Ramniklal after $2$ years is given as $A=140000{{\left( 1+\dfrac{8}{100} \right)}^{2}}$ .
$\Rightarrow A=140000\times {{\left( 1.08 \right)}^{2}}$
$\Rightarrow A=163296$
Hence, Mr. Ramniklal will receive a sum of $Rs.163296$ after $2$ years from the bank.
Let the percentage gain of Mr. Ramniklal be $R$ .
So, $R=\dfrac{163296-140000}{140000}\times 100\%$ .
$=\dfrac{23296}{140000}\times 100\%$
$=16.64\%$
So, $R=16.64\%$ .
We can see $H > R$ .
Hence, the percentage gain for Mr. Hiralal was $41.86\%$ and the percentage gain for Mr. Ramniklal was $16.64\%$. Also, the investment of Mr. Hiralal was more profitable.

Note: While calculating the percentage change, the initial value is taken in the denominator. Some students make a mistake of taking the final value in the denominator. Students should take care that we have to calculate compound interest not simple interest.