Expert: Abe Mantell - 1/7/2011

Question
I'm not sure whether or not this is a basic math or algebra category question; so I posted it here.

Is the annual percentage yield (APY) calculation (1 + periodic rate) - 1 a simplified version of (p + periodic rate) - p? If so, shouldn't there be a "p" in front of the calculation as in p((1 + periodic rate) - 1?
If not, what do the 1's represent from the calculation?

For example, the compound interest calculation is p(1 + r)^n. This is simplified from (p + rp).

I thank you for your reply.

Answer
Actually, the APY is (1 + r/n)^n-1
For example...
Suppose an APR of 4% compounded monthly, so r=0.04 and n=12.
Thus, APY=(1+0.04/12)^12-1=0.0407415... or about 4.074%

The first 1 (inside parentheses) represents the original amount (100%),
the second 1 (outside the parentheses) is also the "original" amount, but
we subtract that to get difference between the "original" and "final"
amounts so we know the actual increase...and hence the APY.

Abe