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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:

enter image description here

That's all. Don't solve.

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  • $\begingroup$ heh... a property for only $105k... an interest rate of 4.5%... this exam question was clearly written some time ago $\endgroup$
    – user253751
    Aug 13 at 10:33
  • $\begingroup$ "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 $\endgroup$ Aug 13 at 12:02
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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, $$ \frac{4.5\%}{12} = 0.375\% \quad \textrm{not} \quad 3.75\% $$

How, exactly, interest rates are compounded is a convention. The bank may decide to pay out a share of the annual interest each month, but not pay interest on interest. This seems to be the case in your exercise. So the annual interest is simply divided by the number of months.

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.

I suspect. the simpler version of compounding was adopted for this exercise to make it not too complicated. Otherwise you would have had to calculate 58 different powers of 1.00036748094004369!

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