Clarissa wants to buy a new car. Her loan officer tells her that her annual interest is 8%, compounded continuously, over a four-year term. Clarissa informs her loan officer that she can make equal monthly payments of $225. How much can Clarissa afford to borrow?
I tried to solve this problem twice using $$P' = (2/25)P - 2700, P(4) = 0, P(0) =\ ?$$ and $$P' = (2/25)P - 225, P(48) = 0, P(0) =\ ?$$ and ended up with two different answers for $P(0)$. Which setup, if either, is correct?
Given that the problem appears in a differential equations book (in an early section), is it safe to assume that the "equal monthly payments" are actually being paid continuously, rather than discretely at the end of each month, or can the compounding frequency and payment frequency still be operating according to two different "clocks"?