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# 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: $$k=3086.64\ /\text{year}$$; $$1259.92$$

Differential Equations