[ELI5] Difference between APY and APR?
In: Economics
So say you have a 12% interest rate per year.
On the surface, that would seem to indicate that if you owed $1000, you would be charged 12% or $120 per year because of interest.
But generally, that 12% per year is split into 1% per month.
Now, if you imagine that you didn’t actually pay anything, and just let that build up over a year, then on month 1 you would be charged $10 dollars, an exact 1% of $1000.
But on month 2, you would be charged 1% of $1010, or $10.10, because you are now paying interest on not only the initial $1000, but also the additional $10.
Month 3 you are charged 1% of $1020.10 or $10.20.
So on and so forth.
In the end, what you end up paying is the same as 12.7% interest applied all at once at the very end ($127), rather than what seemed to be 12%.
APR is that tricky way of doing things, where you have to break payments into months and then compound the interest each month. APY is the “honest” way of displaying how much interest you’ll actually be paying.
—–Side Tangent——
The actual formula for this compound interest is P x (r/n)^nt
Where P is the initial loan or investment
r is the interest rate (1% = 0.01)
n is the number of times the interest is compounded in a given time period (12 times for once per month for one year)
and t is the number of times the compounding occurs.
So for example, 2 years of month compounding at 12% annually would appear as
P x (0.12/12)^(12 x 2) or P x (0.01)^24
The interesting thing I find about this is that if you decrease that month down to weeks or days or hours or minutes, all the way down to *continuously*, the total interest does not approach infinity, but instead approaches
Pe^rt
Where e is Eulers number, or about 2.7.
This also appears *everywhere* in science and in the natural world when describing how things grow or decay over time.
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