# How to convert non-annual interest rate to annual interest rate?

If a student makes monthly deposits of 1,200 into an account with a nominal annual interest rate of 4.5% compounded monthly, will he have enough after 5 years to purchase a $105,000 property in cash? I already have the solution. My question is not to solve anything! I just want to understand why did he use the following to find the annual effective interest rate i = 4.5% / 12 = 3.75% and the Number of compounding periods he used is 60 Why he didn't use the following standard formula: That's all. Don't solve. • heh... a property for only$105k... an interest rate of 4.5%... this exam question was clearly written some time ago Aug 13, 2021 at 10:33
• "nominal annual interest rate", i think by nominal its mean the average. so it is compounded annualy. The months are aproximated by a "nominal" rate. with thtat assumtion is not necesary to handle monthly... but still he prefers using 0.045/12=0.00375 Aug 13, 2021 at 12:02

Your question is a little confusing. The annual interest rate is already given. It's 4.5%. What is done in the calculation is looking for the monthly rate that, when compounded, gives you the annual rate. So, it's reverse compounding. Also, $$\frac{4.5\%}{12} = 0.375\% \quad \textrm{not} \quad 3.75\%$$
Alternatively, it could decide to pay interest on interest, too. In that case the monthly interest rate that gives you 4.5% after a year is. $$^{12}\sqrt{1 + 4.5/100}-1 = 0.0036748094004369 = 0.36748094004369\%$$ which is the reverse application of the formula in the picture.