How to Calculate Compound Interest?

Compound Interest Method

New balance = Principal x [(1 + rate) raised to the power of time]

P(n) = P(0)*(1+r)^n

Principal, P(0) is the money invested
Rate, r = the periodic rate e.g. 12% per annum or 12% per year i.e. 0.12
n = time, which may be days, months, years (but usually either month or years)

The interest portion would be P(n) – P(0)

So as an example, what is the interest on $100 invested for 5 years at 12% per annum

P(5) = 100*(1+0.12)^5
P(5) = 100*1.12^5
P(5) = 100*1.7623
P(5) = 176.23

Thus interest = 176.23 – 100 = $76.23

Another example using the same scenario above but the interest is 12% per annum paid semiannually (twice per year) for 5 years
P(0) = 100
r = 12%/2 = 6% or 0.06
n = 5*2 = 10 payments

P(10) = 100*(1+0.06)^10
P(10) = 100*1.06^10
P(10) = 100*1.7908
P(10) = 179.08

Thus interest = 179.08 – 100 = $79.08

So what is a “power”?
When I wrote 1.12^5, that is the same as saying 1.12 x 1.12 x 1.12 x 1.12 x 1.12. There is a function on the calculator which simplifies that computation. On some it looks like “^” while on others it is a “y” with a small “x” in the top right hand corner.

Hope this helps.