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Math Help - Loans and Interest

  1. #1
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    Exclamation Loans and Interest

    Jim takes out a loan for $5,000 compounded monthly at 5%annual interest and his friend Mark takes out a loan the same day for $6,000 compounded monthly at 3% annual interest:

    1) When will the amount of payments made by Jim be equal to Mark's payments?

    2) What is this amount?
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  2. #2
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    Use the classic compound interesting formula

    P_t = P_0 \left(1+ \dfrac{r}{n}\right)^{nt}

    Where:

    • P_t is the amount at time t
    • P_0 is the initial amount (t=0)
    • r annualised interest rate
    • n number of compounds per year
    • t number of years


    Can you fit the information you've been given into that formula? If you use it once for Jim and once for Mark then you can set the two equations equal to each other and solve for t
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  3. #3
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    Quote Originally Posted by ksiemsen24 View Post
    Jim takes out a loan for $5,000 compounded monthly at 5%annual interest and his friend Mark takes out a loan the same day for $6,000 compounded monthly at 3% annual interest:
    1) When will the amount of payments made by Jim be equal to Mark's payments?
    2) What is this amount?
    Please CLARIFY.
    Do you mean: when will both loan balances be equal?
    Why do you say "payments" if these loans are not repaid by regular loan payments?
    Do you mean monthly payments are made (interest compounds monthly)?
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  4. #4
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    Lightbulb Loans and Interest

    Harry takes out a loan at $5,000 compounded monthly at 5% annual interest and his friend Carrie took out a loan the same day for $6,000 compounded monthly at 3% annual interest:

    1) When will the amount of payments that Harry makes on his loan equal the amount of payments that Carrie makes on her loan?

    2) What is the amount that that will be equal?


    (I posted this question differently before, and was asked to clarify, but this is how the question was proposed to me verbatim. Please help.)
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  5. #5
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    Well, if you can't answer my questions, then there's nothing I can do.

    Your problem is a bit like:
    Jack has 50 apples and John has 60 apples.
    If they both eat apples for a while, with John eating a little
    faster than Jack, when will they have an equal number of apples?

    IF "somehow" the intent is to find out when the loan balances will be
    equal IF no payments are made, then:
    5000(1 + .05/12)^n = 6000(1 + .03/12)^n
    Solve for n.
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