Question

Explain why the amount of money in the account at the end of t years is given by the formula:

P = P0(1 + r/n)^nt

Answer 1

Explanation:

The initial amount invested is P0

Say it is compounded periodically either quarterly or monthly or semi annually with interest r%

If for a period interest is r%

Then after first period principal = principal+simple interest

=
`P_(0)+(P_(0)r )/(n)`

where n is the no of times in a year it is compounded. n = 4 if quarterly, 12 if annually, etc

At the end of II period we have

Principal =
`P_(0)+(P_(0)r )/(n)`

So for interest again the process is repeated

Thus we repeat this nt times which result in power with nt

Hence the formula