Difference in Growth Functions y = A*(1+r)^t and P(t) = Po(e^(rt))

[BigNate]

Hello,

Can someone please explain to me the difference between the following functions:

y = A*(1+r)^t

P(t)=Po(e^(rt))

Thanks!

 

[Dr.Peterson]

Can someone please explain to me the difference between the following functions:

y = A*(1+r)^t

P(t)=Po(e^(rt))

Thanks!

They are entirely equivalent in a mathematical sense, but expressed in terms of different parameters so that they are used in entirely different circumstances.

The first is used for annually compounded interest; A is the initial amount, r is the annual interest rate, and t is the number of years. It is assumed that t is an integer, since interest is compounded only after each whole year. But it could be used for any exponential growth for which you know the equivalent parameters, without that restriction.

The second is use for continuously compounded interest, or for any exponential growth. Po is the initial amount (principal), r is the nominal interest rate (instantaneous growth rate), and t is the time.

You could use logarithms to put either formula in the other form; you would find that "r" is different, but A is equivalent to Po.

You may have more specific questions in mind; if this is related to a class, you should be able to find the general answer in your textbook, and can ask us questions is doesn't answer.

 

[tkhunny]

Some presentations refuse to accept any base but 'e'.

Read my signature. That's how I feel about that.