Question

what is the interesting thing we learn from financial mathematics course

related to interest and compound interst

Answer 1

We all know simple and compound interest

I am just briefing it below

Simple : - when interest is calculated every year on the original principal.

Compound : - the interest is added to the principal at the end of each period to arrive at the new principal for the next period .

Whether is it compound or simple we can calculate the interest with given principal amount ( P ) , given rate of interest ( r ) and number of periods ( n )

But what about a situation when a person wants to reinvest his money within a period. He can reinvest as many times as he wanted. How we will calculate interest here.

That's interesting....!

NOTE : - If there are n period and every period is divided into m subgroups ( I.e money is reinvested m time in one period )

If r is the rate of interest for one period. Then the value of P after n period where every period is divided into m subgroups is

$A= P\left ( 1+\frac{r}{m} \right )^{mn}$

Explanation: -

At the end of 1 period the amount P become

$A= P\left ( 1+\frac{r}{m} \right )^{m}$

Thus the value of P after n period

$A= P\left ( 1+\frac{r}{m} \right )^{mn}$