Hi there, I'm tying to figure out how much interest I would pay on 20,000 if it was 25% compounded daily.
Hi,
If the annual interest rate is 25%, that is 0.25, then the daily interest rate is 0.25/365 = 0.0006849315. So that I don't have to type these long numbers I am going to use letters. I am going to use r for the annual interest rate (r = 0.25), P for the principle (P = $20,000) and n for the number of times compound (n = 365). The daily interest rate is then r/n (this is 0.0006849315).
You borrow $20,000 so at the end of the first day you owe $20,000 plus the interest. Thus at the end of the first day you owe
P = P(1 + r/n)
Hence at the beginning of the second day you owe P(1 + r/n), and thus at the end of the second day you owe P(1 + r/n) plus the interest on that amount which
P(1 + r/n) = P(1 + r/n)(1 + r/n) = P(1 + r/n)2
Now I hope you can see what happens. At the beginning of the third day you owe P(1 + r/n)2 and thus at the end of the third day you owe
P(1 + r/n)2 = P(1 + r/n)3
For P = $20,000, r = 0.25 and n = 365 I get