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Math Help - please help me solve this annuity problem

  1. #1
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    please help me solve this annuity problem

    A student receives a federally backed student loan of $ 600 at 3.5% interst compounded monthly. After fishing college in 2 years, the student must amortize the loan in the next 4 years by making equal monthly payments.what will the payments be and what total intersest will student pay?please help me! thanks
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  2. #2
    MHF Contributor
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    How many times have I said this? You MUST learn to use Basic Principles. Draw a map and reason it out.

    i = 3.5% = 0.035
    i^{(12)} = 0.035/12 = 0.00291666666... <== Monthly interest rate.
    Note: I'll just use 'i' in order to make the notation more convenient. Just remember this is the MONTHLY rates of interest.
    t = time in years

    t = 0 ==> 600.00 <== There's the loan.

    t = 2 ==> 600.00 \cdot (1+i)^{24} <== There's the value after two years (24 months).

    Pull your Annuity Immediate formula out of your hat...(or learn to derive it!)

    P = Equal Monthly Payment
    v = \frac{1}{1+i} = 0.997091815

    Note: Remember, this is a monthly rate. 'v' is the MONTHLY rate of discount.

    600.00 \cdot (1+i)^{24} = P \frac{v - v^{49}}{1-v}

    or

    600.00 \cdot (1+i)^{24} = P \frac{1 - v^{48}}{i}

    Solve for 'P' and you nearly are done.
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  3. #3
    MHF Contributor
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    In case you are wondering what "draw" means...

    Here is an example.

    Time Value of Money

    It's just a simple map to help you see when money moves and when it has what value.

    In your case, you have +$600 at t = 0 months and -$P at each of months 25 - 72.
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