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Math Help - Question on Calculus homework problem

  1. #1
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    Question on Calculus homework problem

    A $300, 000 loan is to be repaid over 30 years in equal monthly installments of $M ,
    beginning at the end of the first month. Find the monthly payment M if the loan
    annual rate is 5% compounded monthly.

    Hint: Find an expression for the present value of of the sum of all of the monthly
    payments, set it equal to $300,000 and solve for M .

    Need to find using series I think. We haven't done anything like this in class and I looked through the book and their is nothing that will help, basically I'm 100% lost...
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  2. #2
    MHF Contributor
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    Re: Question on Calculus homework problem

    You MUST have SOME idea. You simply MUST. If nothing else, you could try the hint.

    i = 0.05 -- This is annual interest
    j = i/12 = 0.00416666... -- This is monthly interest
    v = 1/(1+j) = 0.995850622406639 -- This is the monthly discount factor

    That's all you need. Now build it.

    300000 = M*(v + v^2 + v^3 + ... + v^360)

    Can you add that up inside the parentheses?

    Note: This is a geometric series.
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