Hi guys, I’m watching this video currently and want to check something.
I’m an economics teacher and have always taught my pupils that when you have a compound interest rate, let’s say 4% a year, you cannot simply say that it equals 1% per quarter (so 4% per year divided by 4 quarters in a year). Rather, it should be calculated by 1.04^1/4. However in these videos I see that 1% per quarter is calculated from 4% a year simply by dividing.
Does this mean that on the GRE the latter method (the one in the video) is always used so I should ignore the method I described myself?
Can you give a relevant screenshot in the video (not sure where in the video you exactly need help)?
Also: linking videos on PrepSwift doesn’t work the way you expect it to. Just give the name. Include a screenshot in any case since not everyone would have access to it.
If I understand you correctly, yes.
That being said, I’ve never heard your method (i.e, A = P (1 + r)^{t/4} ), where t is the number of periods, A is the amount after compounding, and P is the initial amount invested, be used to find the interest in a compound period. Even in finance-related modules at university, I’ve been taught Greg’s way (i.e, A = P (1 + r/4)^{t} ).
Well I’ll show you why it works.
Imagine $1000 at 12% annual compound interest and 1 year
1000 x 1.12 = 1120, so interest is 120. But 12% a year is not the same as 3% per quarter. You simply should not divide percentages (unless it’s simple interest)
Now convert the compound period to a quarter with my method
1.12^(1/4) = 1.02873… per quarter
1000 x 1.02873^4 = 1120, so interest is 120
While if you do
1000 x 1.03^4 = 1125.51
Cannot imagine this is not taught in university finance classes but maybe I’m not explaining properly or explaining something differently than the question is asking?
It is because we divide into equivalent compounding periods. Indeed I get what you are saying, but this isn’t backed up with what I’ve learned.
We can even go further and show that your method cannot be correct. Let’s start from the method I’m familiar with, where t is the number of years and r is the rate:
P = A \left(1 + \frac{r}{n} \right)^{tn}
Now, what happens as n \rightarrow \infty (i.e, as we move to a continuous compounding model):
\lim_{n \rightarrow \infty} P \left(1 + \frac{r}{n} \right)^{tn} = P e^{rt}
This is consistent with the definition of continuous compounding (this can be verified by setting up a differential equation P' = Pr where P' is the derivative of the principal).
Now consider your method. You are saying that
\lim_{n \rightarrow \infty} P \left({1 + r} \right)^{t} = P (1 + r)^t
which is not the same (in particular, this is only true for yearly compounding periods).
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Ok I’m not sufficiently deep into finance to understand this but I believe you 
Only disagree with the method not being correct (probably for certain type of cases it is) as it’s simply part of the curriculum we teach and so that would mean all economics students in the Netherlands (while it only houses 16 million inhabitants, so not too much to worry about on the world-scale) is being taught non-existent compound interest calculations 