Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I was wandering what the difference was between compounding interest when they use bi-annual and semi-annual and hence how to change your value of i

I think semi-annual means twice in 1 year so your i would be i/2? and then you would multiply your years by two as well

however im not sure how to deal with bi-annual, i think it means once every 2 years so would you take you i and divide it by 0.5 as well as your number of years?

share|cite|improve this question
up vote 1 down vote accepted

I assume you are using the formula for compound interest: $$A = P \left(1 + \frac{i}{n}\right)^{nt}$$ where $A$ is the future value, $P$ is the present value, $i$ is the annual interest rate (as a decimal), $n$ is the number of times compounded per year and $t$ is the length of time in years. It is very important here that the question states interest as the annual interest rate.

Semi-annual means twice in one year. Therefore, your $n$ will equal 2. Hence, your formula becomes $$A = P \left(1 + \frac{i}{2}\right)^{2t}.$$

You are correct that bi-annual means once every two years. Therefore, the interest is compounded "half" a time per year (1 compounding every 2 years for $\frac{1}{2}$). Now we have $n = \frac{1}{2}$ and $$A = P \left(1 + \frac{i}{\frac{1}{2}}\right)^{\frac{1}{2}t}$$

share|cite|improve this answer
Also for interest if one is trying to convert between interest rates we use the formula $$(1+i) = (1 + \frac{j}{n})^{n}$$ where $i$ is the effective interest for one year, and $j$ is the nominal interest compounded $n$ times per year. (If one wants to find the effective interest for the $n$th period one just has to find the value $j/n$. – TJ Lockwood Mar 27 at 19:47

Your Answer


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.