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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?

Daniel Feinstein
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1 Answers1

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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 $$A = P \left(1 + \frac{i}{\frac{1}{2}}\right)^{\frac{1}{2}t}$$

Kris Williams
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  • 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 $j/n$. – TeeJ Lockwood Mar 27 '16 at 19:47
  • "Biannual" means twice a year. "Biennial" means once every two years. – smcc Dec 05 '18 at 10:39