This one is exponential decay and is a different type of equation to compound interested. For this one you'd use the two main formulae in exponential decay:

(eq1)

(eq2)

These can be combined into

Where

- is amount left at time t
- is initial amount at t=0
- is the decay constant
- is time

For compound interest you can't really use e as a base because it is not strictly accurate:Here's a problem I made up:

You deposit $500 into an account. You recieve a compound interest rate of 5% every 3 months. How much will you have after 1 year?

so using e is only accurate for an infinite series.

Instead you'd use something like

where

- amount of N at time t
- amount at time 0
- growth rate
- time

Because there are 4 lots of 3 months in one year interest will be compounded 4 times so t=4.

Edit:

Where,

*P = principal amount (initial investment)

*r = annual nominal interest rate (as a decimal)

*n = number of times the interest is compounded per year

*t = number of years

*A = amount after time t

The above is a more general formula for what I put.