Question

Mr. Sayyad kept Rs. 40,000 in a bank at 8% compound interest for 2 years. Mr. Fernandes invested Rs. 1,20,000 in a mutual fund for 2 years. After 2 years, Mr. Fernandes got Rs. 1,92,000. Whose investment turned out to be more profitable?

Answer 1

Hint: Find the total amount of both Mr. Sayyad and Mr. Fernandes at the end of 2 years and then calculate the percentage increase from the initial sum for both.

Complete step-by-step answer:

According to the question, Mr. Sayyad kept Rs. 40,000 in a bank at 8% compound interest for 2 years. We know that the total amount for a sum of money compounded annually can be calculated using formula:
$ \Rightarrow A = P{\left( {1 + \dfrac{r}{{100}}} \right)^t}$, where P is the initial principal, r is the rate of compound interest and t is the time period in years.

For the given case, $P = 40000$, $r = 8\% $ and $t = 2{\text{ }}years$. Substituting these values, we get:
$
   \Rightarrow A = 40000 \times {\left( {1 + \dfrac{8}{{100}}} \right)^2}, \\
   \Rightarrow A = 40000 \times {\left( {1.08} \right)^2}, \\
   \Rightarrow A = 46656 \\
$

The standing amount after 2 years is Rs. 46656. We can calculate compound interest:
$ \Rightarrow $Compound Interest $ = $Amount $ - $ Principal,
$ \Rightarrow $Compound Interest $ = $46656 $ - $ 40000 $ = $6656.
So, compound interest gained after two years is Rs. 6,656. Profit percentage is:
$
   \Rightarrow {\text{Profit}}\left( \% \right) = \dfrac{{{\text{Profit}}}}{{{\text{Principal}}}} \times 100, \\
   \Rightarrow {\text{Profit}}\left( \% \right) = \dfrac{{6656}}{{40000}} \times 100, \\
   \Rightarrow {\text{Profit}}\left( \% \right) = 16.64\% \\
$

Hence, Mr. Sayyad enjoys 16.64% profit on his investment.
Further, Mr. Fernandes invested Rs. 1,20,000 in a mutual fund for 2 years and after this time period his principal amounts to Rs. 1,92,000. So his profit is:
$
   \Rightarrow {\text{Profit}} = 192000 - 120000, \\
   \Rightarrow {\text{Profit}} = 72000 \\
$

Mr. Fernandes’ profit percentage:
$
   \Rightarrow {\text{Profit}}\left( \% \right) = \dfrac{{72000}}{{120000}} \times 100, \\
   \Rightarrow {\text{Profit}}\left( \% \right) = 60\% \\
$

Hence, Mr. Fernandes enjoys 60% profit on his investment.

Clearly, Mr. Fernandes’ investment is more profitable.

Note: Profit percentage is always calculated over the initial sum. Further, in the case of compound interest, the amount standing at the end of a compounded period works as a principal for the subsequent compounding period.