Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I would like to be able to calculate the interest rate that is compounded for a given total interest rate, and number of compounding events.

TotalInterestRate = ((1+CompoundingRate/#CompoundingEvents)^#CompoundingEvents)-1

Basically would like to solve this equation for Compounding Rate.

For a more concrete example, calculating the Monthly Interest Rate from a given APY. The formula for APY given a Monthly Interest Rate would then be.

APY = ((1+InterestRate/12)^12)-1

What would be a good way to go about solving this equation?

share|improve this question

1 Answer 1

If we refer to the effective interest rate as $r$ (what you call the total interest rate) and we refer to the nominal interest rate as $n$ (what you call the compounding rate) and the compounding frequency as $N$, the formula you have is $$r=\left(1+\frac{n}{N}\right)^N-1$$ To solve for $n$:

$$\begin{align} r+1 &=\left(1+\frac{n}{N}\right)^N\\ \sqrt[N]{r+1}&=1+\frac{n}{N}\\ \sqrt[N]{r+1}-1&=\frac{n}{N}\\ N\left(\sqrt[N]{r+1}-1\right)&=n\\ \end{align}$$

share|improve this answer
    
Same, but using the symbols in the question: $\mbox{InterestRate} = 12(\sqrt[12]{\mbox{APY}+1}-1)$. –  copper.hat Jul 6 '12 at 6:10
    
@copper.hat I believe that is for a more specific example than the OP firsts asks about. –  alex.jordan Jul 6 '12 at 6:14
    
You are correct, I missed that... –  copper.hat Jul 6 '12 at 6:16
    
+1 for unintentionally reminding me that "effective" and "real" interest rates are not the same thing. –  John Joy Dec 3 at 14:28

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.