Continuous Monthly Payments
I am just beginning differential equations, so this is probably a very simple question, please forgive my ignorance! Here is the question:
$12,000 is borrowed. The loan is to be paid in 60 equal monthly installments at an interest rate of 5% per year. If the payments are actually made continuously at the necessary rate to pay off the loan in 60 months. Determine the continuous rate per month that would be required.
I believe the debt should grow using this equation:
y = value of the debt
t = time
(1/y)(dy/dt) = k
However, I do not know how to simultaneously consider the continuous monthly payments forcing the debt downward.
Also, if anyone knows a good resource on modeling situations with differential equations, please let me know because my textbook does not describe this very well.
Any help would be appreciated.