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# Kelly and friends buy a house after graduating from college and borrow $200,000 from the bank to pay for it. Suppose that the bank charges 12% annual interest on the outstanding principle and that Kelly's group plans to make monthly payments of d =$ 2,500 to the bank. Call A(t) the amount of money the group still owes the bank. (a) What is the initial value problem that describes A(t)? (b) Solve the IVP in part (a). (c) How long will it take Kelly and friends to pay off the loan'?

Solution

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Given: $A_0 = \ 200,000$

$a = \ -2,500$
$r = 0.12$ annually or $\dfrac{0.12}{12} = 0.01$ monthly.

We have $\boxed{ \dfrac{dA}{dt} = r A + a , \; \textrm{where} \; A(0) = A_0 }$

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