What is the difference between compound interest and exponential growth?

Question

I'm doing GCSE maths- ao could you keep it as simple as possible please.
Thanks

Answer 1

I would say that compound interest is a form of exponential growth.
the exponential functions are the family of functions that have the form a^x, where a > 1.
Compound interest is modeled as an exponentila growth problem. Another phenomenon that can be modeled as exponential growth is population growth.
In other words, compound interest is an application of exponential growth.

Answer 2

They have some similar features - that is to say, the time factor being an index (to the power of).

The formula for compound interest is:
At = A0 (1+R/100)^t

In other words, the amount at time t (At) equals

the initial amount (A0) or amount at time 0
times (100% + interest rate (R) as a percentage) to the power of the time (t) taken. The units of time t depends on the way the interest is calculated and is usually in years.

Whereas exponential growth is usually described in doubling time (t). If you start at time 0 with a certain number of organisms (N0) and you leave them for a certain number of doubling times (t) - note that this will be different for many organisms and is often in a matter of minutes to days - you will end up with a bigger number of organisms Nt.

Nt = N0(2)^t

You could say this is a special form of compound interest where the R is 100% (or perhaps compound interest is a special form of exponential growth where the base rate is not using a doubling time).

The Nt in exponential growth tends to grow much faster than the At in compound interest. Organisms have a faster rate of growth (R) and the time intervals being studied are much shorter.

Answer 3

Compound interest :
if you interest $m with rate = r% per period so the total money after n periods = m(1+r%)^n
Exponential growth :
If a comunity with population p increases with rate r then the final population after n periods F = p e^(r n)
More details in:
http://www.algebralab.org/Word/Word.aspx?file=Algebra_ExponentialGrowth.xml