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Math Help - differential equation involving interest

  1. #1
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    differential equation involving interest

    A worker borrows usd 550,000 at an annual interest rate of 6% to purchase a house from a bank. Suppose he make an arrangement to pay the bank k usd per month. Let S(t), measured in usd, be the balance due on the loan at any time t, measured in years.
    (a) Write a differential equation to calculate the amount of loan left to be
    paid.
    (b) Solve for S(t).
    (c) If the worker wishes to pay off the loan in 5 years, find the value of the monthly payment k usd.
    (d) What is the total amount paid over the life of the loan and hence find the
    total interest payment made?

    i know that the de :

    S(t) = S_0*e^{rt}


    dS/dt= r*S_0*e^{rt} = r*B(t)

    IS THIS CORRECT FOR Q (a) and (b)


    But from here how can i know the total paid over the life of the loan .... and the total interest payment????

    is that occur when set t ----> infinity?????


    plz help me.......
    Last edited by bobey; March 9th 2010 at 10:33 PM.
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