Question

A person wants to invest Rs. 100000 in a fixed deposit scheme for 2 years. His financial advisor explained to him two types of schemes first is yielding 10% p.a. compounded annually, second is yielding 10% p.a. compounded semi-annually. Which scheme is better and why? Why investment is important for future life?

Answer 1

Hint: This question is the simple example of compound interest calculations. We need to compute the compound interest in two different time frames. And hence we can decide about the better investment plan based on their returns.

Complete step-by-step answer:
We know that total amount in the case of compound interest can be calculated by the formula as follows:
Amount = $P{(1 + \dfrac{r}{{100 \times n}})^{n \times t}}$
Where P is Principal Amount
n= No. of instalments in one year
t= Total number of years.
r = rate of interest.
For case-1:
r= 10
n=2
t=2
So, substituting these values in above formula, we get,
\[
Amount = 100000 \times {(1 + \dfrac{{10}}{{100 \times 1}})^2} \\
\Rightarrow Amount = 100000 \times \dfrac{{11}}{{10}} \times \dfrac{{11}}{{10}} \\
\Rightarrow Amount = 121000 \\
\]
For case-2:
r= 10
n=1
t=2
So, substituting these values in above formula, we get,
\[
Amount = 100000 \times {(1 + \dfrac{{10}}{{100 \times 2}})^{2 \times 2}} \\
\Rightarrow Amount = 100000 \times {(\dfrac{{21}}{{20}})^4} \\
\Rightarrow Amount = 100000 \times \dfrac{{21}}{{20}} \times \dfrac{{21}}{{20}} \times \dfrac{{21}}{{20}} \times \dfrac{{21}}{{20}} \\
\Rightarrow Amount = 121550.625 \\
\]
It is clear that the amount in case-2 is more than that of in case-1.
Therefore the second schedule is a better scheme.
 Investing is to ensure our present as well as future through long-term financial security. The money which one can generate from the investments will definitely provide financial security and income. There are many ways for investments such as stocks, bonds, FDs, and ETFs etc.

Note: This problem is explaining the FD investment in two different time period plans. One is annually and the other one is semi-annually. Similarly, we may have other time durations like monthly, bimonthly, or even quarterly.