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Math Help - Debt Payment Question

  1. #1
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    Debt Payment Question

    One of my hw questions I can't quite figure out:
    Debt of $3500 due in 4 years and $5000 due in 6 years is to be repaid in a single payment of $1500 now and 3 equal payments that are due each consecutive year from now. If the interest rate is 7% compounded annually, how much are each of the equal payments?

    It would be nice if someone could explain how to answer the question instead of just giving the answer but any help is appreciated
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  2. #2
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    Write an equation of value using the present as the comparison date. Thus

    <br />
\left[ {3,500\left( {1.07} \right)^{ - 4}  + 5,000\left( {1.07} \right)^{ - 6} } \right] - 1,500 = R\frac{{1 - \left( {1.07} \right)^{ - 3} }}{{0.07}}<br />

    Now solve for R.
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  3. #3
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    Sir Jonah, another show of Latexity beauty
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  4. #4
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    Quote Originally Posted by Wilmer View Post
    Sir Jonah, another show of Latexity beauty
    Indeed it is Sir Wilmer, indeed it is.
    So when do you think you can join us and make your own "Latexity beauty" posts like you promised?
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  5. #5
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    Quote Originally Posted by lil_cookie View Post
    One of my hw questions I can't quite figure out:
    Debt of $3500 due in 4 years and $5000 due in 6 years is to be repaid in a single payment of $1500 now and 3 equal payments that are due each consecutive year from now. If the interest rate is 7% compounded annually, how much are each of the equal payments?

    It would be nice if someone could explain how to answer the question instead of just giving the answer but any help is appreciated
    This is the rough method I use to find the ball park.
    7% of $3500 is $245; for 4 years it is $980
    (note this is without the compounding.)
    7% of $5000 is $350; for 6 years that makes $2100

    Total payback: $3500 + $980 + $5000 + 2100 is $11580.
    Subtract the $1500 leaves $10080.

    You are going to repay it in 3 installments per year for five years or 15 payments.

    $10080/15 is about $672 every four months, for the years following the first one.

    Now that you're in the ball park, you can use the appropriate formula to get a much more precise value.

    If the interest rate is 7% compounded annually
    that implies that NO interest in added at the time a payment is made, which is three times each year.



    An accountant I spoke with indicated that this co-mingling of the different accounts is not an acceptable method -- what's a banker know about math, anyway?



    This is confusing to me
    ... is to be repaid in a single payment of $1500 now
    Does this mean that you borrow $3500 and $5000 and then immediately (now) repay $1500 without having the use of it for year?




    Account1: $3500 for 4 years at 7% per year, with an initial payment and the remainder repaid in 3 installments per year for the following three years after this year.

    Account2: $5000 for 6 years at 7% per year, with an initial payment and the remainder repaid in 3 installments per year for the following five years after this year.

    The necessity for equal repayment amounts for un-equal borrowed amounts is what makes this an intricate problem.

    Could you clarify your problem?
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  6. #6
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    Quote Originally Posted by lil_cookie View Post
    > Debt of $3500 due in 4 years and $5000 due in 6 years

    Looks this simple to me (to closest dollar):

    3500/1.07^4 = 2670
    5000/1.07^6 = 3332

    So owing today = 2670 + 3332 = 6002

    > is to be repaid in a single payment of $1500 now

    Now owing today = 6002 - 1500 = 4502

    > and 3 equal payments that are due each consecutive year from now. If the interest rate
    > is 7% compounded annually, how much are each of the equal payments?

    So we need the annual payment that'll pay that off in 3 years:
    4502 * .07 / (1 - 1 / 1.07^3) = 1715
    (same results with Sir Jonah's formula)
    .
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  7. #7
    Member jonah's Avatar
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    Quote Originally Posted by aidan View Post

    Quote Originally Posted by lil_cookie View Post
    One of my hw questions I can't quite figure out:
    Debt of $3500 due in 4 years and $5000 due in 6 years is to be repaid in a single payment of $1500 now and 3 equal payments that are due each consecutive year from now. If the interest rate is 7% compounded annually, how much are each of the equal payments?

    It would be nice if someone could explain how to answer the question instead of just giving the answer but any help is appreciated
    This is the rough method I use to find the ball park.
    7% of $3500 is $245; for 4 years it is $980
    (note this is without the compounding.)
    7% of $5000 is $350; for 6 years that makes $2100

    Total payback: $3500 + $980 + $5000 + 2100 is $11580.
    Subtract the $1500 leaves $10080.

    You are going to repay it in 3 installments per year for five years or 15 payments.???

    $10080/15 is about $672 every four months, for the years following the first one.

    Now that you're in the ball park, you can use the appropriate formula to get a much more precise value.

    that implies that NO interest in added at the time a payment is made, which is three times each year.


    An accountant I spoke with indicated that this co-mingling of the different accounts is not an acceptable method -- what's a banker know about math, anyway?



    This is confusing to meDoes this mean that you borrow $3500 and $5000 and then immediately (now) repay $1500 without having the use of it for year?




    Account1: $3500 for 4 years at 7% per year, with an initial payment and the remainder repaid in 3 installments per year for the following three years after this year.

    Account2: $5000 for 6 years at 7% per year, with an initial payment and the remainder repaid in 3 installments per year for the following five years after this year.

    The necessity for equal repayment amounts for un-equal borrowed amounts is what makes this an intricate problem.

    Could you clarify your problem?
    Sir Aidan, reading your strange "ballpark" analysis made me realize that you could really use a stronger background in finance/investment mathematics. You are definitely nowhere near the ballpark (see my earlier post and Sir Wilmer's analysis). You might want to have a look here.
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