Quandaries and Queries 

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 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 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 For P = $20,000, r = 0.25 and n = 365 I get 

