These can be combined into
- 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
- amount of N at time t
- amount at time 0
- growth rate
Because there are 4 lots of 3 months in one year interest will be compounded 4 times so t=4.
*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.