Hello! I'm working on a finance-related problem, and I'm not sure that I'm solving the ODE well!
Here's the prompt:
A certain college graduate borrows $8,000 to buy a car. The lender charges interest at an annual rate of \(10\%\). Assuming that interst is compounded \(\sf continuously\), and that the borrower makes payments \(\sf continuously\) at a constant annual rate \(k\), determine the payment rate \(k\) that is required to pay off the loan in \(3\) years. Also, determine how much interest is paid during the \(3\)-year period.
The answers: \(k=$3086.64\ /\text{year}\); \($1259.92\)

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