<p>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, <em>when compounded</em>, gives you the annual rate. So, it's <em>reverse</em> compounding. Also,
<span class="math-container">$$
\frac{4.5\%}{12} = 0.375\% \quad \textrm{not} \quad 3.75\%
$$</span></p>
<p>How, exactly, interest rates are compounded is a convention. The bank may decide to pay out a <em>share</em> 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.</p>
<p>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.
<span class="math-container">$$
^{12}\sqrt{1 + 4.5/100}-1 = 0.0036748094004369 = 0.36748094004369\%
$$</span>
which is the reverse application of the formula in the picture.</p>
<p>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!</p>

CC BY-SA 4.0
2021-08-13T16:15:10.173Z
2021-08-13T16:15:10.173Z
BrsG
<p>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?</p>
<p><strong>I already have the solution.</strong></p>
<p><strong>My question is not to solve anything!</strong></p>
<p>I just want to understand why did he use the following to find the annual effective interest rate</p>
<p>i = 4.5% / 12 = 3.75%</p>
<p>and the Number of compounding periods he used is 60</p>
<p>Why he didn't use the following standard formula:</p>
<p><a href="https://i.sstatic.net/VL9sc.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/VL9sc.png" alt="enter image description here" /></a></p>
<p>That's all. Don't solve.</p>

CC BY-SA 4.0
2021-08-13T10:33:29.030Z
heh... a property for only $105k... an interest rate of 4.5%... this exam question was clearly written some time ago
Criticize SE actions means ban
CC BY-SA 4.0
2021-08-13T12:02:45.313Z
"**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
Alfredo Maussa
<interest-rate>
How to convert non-annual interest rate to annual interest rate?
OMAR
# How to convert non-annual interest rate to annual interest rate?

(Asked by: username_0 on 2021-08-13)

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](https://i.sstatic.net/VL9sc.png)](https://i.sstatic.net/VL9sc.png)

That's all. Don't solve.

**Tags:** interest-rate

> **Comments:**
> **username_1**: heh... a property for only $105k... an interest rate of 4.5%... this exam question was clearly written some time ago  
> **username_2**: "**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  

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## 1 answers

### Answer by username_3 on 2021-08-13. Score: 2

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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