# Question about the investment calculator interest rate

I have a quick question question about this investment calculator. It is the website calculator.net/investment calculator Basically I put in my starting amount of investment is 4800, for 1 year, with a return rate of 10%, compounded annually. And I add a contribution of 100 dollar at the beggining of the month

So I did my calculation I did

\$(4800+100)*(.10/12))\$ to get my interest amount of \$40.833\$

But the calculator says the correct amount of interest is 39.07

I am confused how they get 39.07 for the interest amount. I though if it is 10 compound interest you do .10/12 to get monthly interest. please help.

The interest rate used in the calculator is the effective annual rate or, equivalently, the nominal annual rate compounded annually. To work out the monthly rate `mr` you have to invert the compounding like so:

``````ar = 0.10

mr = (1 + ar)^(1/12) - 1 = 0.00797414

(4800 + 100) * mr = 39.0733
``````

If the interest rate was a nominal annual rate compounded monthly the monthly rate would be calculated as `mr = ar/12`. Then the effective annual rate would be `(1 + mr)^12 - 1 = 0.104713`

Nominal rates are created as multiples of their compounding period to make calculations easier, e.g. `mr = ar/12`. The cost is that, say a 10% nominal annual rate compounded monthly, weekly, or daily all result in different interest accruals over a year.

• I have a quick question so what is ar, is it the annual rate May 1, 2022 at 23:19
• @FernandoMartinez Yes, annual rate (effective or nominal according to context). May 2, 2022 at 8:32