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Back in middle school, We learned that if the interest rate given, r, is annual, it must be divided By the number of times compounded per year, n, to get interest rare per period.

I was reviewing compound interest for a standardised test and it got me thinking. Why is an “annual rate” given in the first place? The interest rate per period applies to a different principal every period so you cant just find that rate by dividing the annually rate equally Into n Period , right? What does, say an interest rate of 10% compounded quarterly, even mean? Is hid something just to confuse you?

J. W. Tanner
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Vulgar Mechanick
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I mean, you can. You just have to take powers. Using your example:

You have annual interest rate $10%$, compounded quarterly. Suppose your principle is $100$, then, after one year, you have:

$$100 \times (1 + \frac{10}{4\cdot 100})^4 = 100 \times (1 + 0.025)^4 = 110.38.$$

This is standard practice in finance, and you should get used to it, so that you don't get swindled. Mess around with some numbers.

At the end, the definitions are just long-standing conventions in banking.

Benjamin Wang
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  • What does that 10% mean though? Even in your example, the actual interest in that year is 10.38% so whats the reason for stating 10%? Why not just give the rate per peiod which makes sense? – Vulgar Mechanick Jun 14 '20 at 13:41
  • Exactly, this might not make sense. However, this is finance, and perhaps things made sense to accountants hundreds of years ago, and the traditions have stuck. I'm not trying to justify it. It is simply the case that if you want to use it, you have to speak their vocabulary. We can say that an annualised rate of return on an investment with the parameters specified is 10.38%, though. – Benjamin Wang Jun 14 '20 at 13:56
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    Oh ok. I just wanted to ensure that this was a matter of convention and that I wasnt missing something. Thank you for clarifying. – Vulgar Mechanick Jun 14 '20 at 14:27