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Math Help - Loan

  1. #1
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    Loan

    James borrowed $5,000 from his friend 2 years ago; and, an additional $3,000 1 year ago. He wants to repay his friend the money that he borrowed plus interest at 8% compounded quarterly.

    a) How much will James have to pay in 2 years time to fully repay his debt if he pays $1,000 to-day & $4,000 1 year from now?

    b) Calculate James' payments if he wants to fully repay his debt with two equal payments - the first 9 months from now & the second 18 months from now.

    Possible formula: Fv=PMT[ (1+i)^n -1 / i ]

    Someone please help me with this question...
    Thanks in advance
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  2. #2
    MHF Contributor
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    Quote Originally Posted by julie View Post
    James borrowed $5,000 from his friend 2 years ago; and, an additional $3,000 1 year ago. He wants to repay his friend the money that he borrowed plus interest at 8% compounded quarterly.

    a) How much will James have to pay in 2 years time to fully repay his debt if he pays $1,000 to-day & $4,000 1 year from now?

    b) Calculate James' payments if he wants to fully repay his debt with two equal payments - the first 9 months from now & the second 18 months from now.

    Possible formula: Fv=PMT[ (1+i)^n -1 / i ]

    Someone please help me with this question...
    Thanks in advance
    Let me use the formula for compound interest.
    A = P(1 +i)^n --------------(1)
    where
    A = amount of investment after n numbers of compounding.
    P = principal or initial value of investment
    i = periodic rate, or relative rate per compounding
    n = number of compoundings.

    a)How much will James have to pay in 2 years time to fully repay his debt if he pays $1,000 to-day & $4,000 1 year from now?
    Today:

    Debt due to the $5000 two years ago.
    8% per annum compounding quarterly, so, i = 0.08/4 = 0.02
    Two years ago, so, n = 2*4 = 8 compoundings.
    A1 = 5000(1+0.02)^8 = $5858.30 today.

    Debt due to the $3000 last year.
    n = 1*4 = 4
    A2 = 3000(1.02)^4 = $3247.30

    So, total debt today = A1 +A2 = 5856.30 +3247.30 = $9105.60
    Paying 1000 today,........ 9105.60 -1000 = $8105.60 balance

    ------------
    After 1 year from today.

    P = 8105.60
    i = 0.02
    n = 1*4 = 4

    New debt = 8105.60(1.02)^4 = $8773.76
    Paying 4000,........... 8773.76 -4000 = $4773.76 new balance

    -----------------------
    For final payment two years from today.
    That is 1 year from next year.

    P = 4773.76
    i = 0.02
    n = 1*4 = 4

    Newer debt = 4773.76(1.02)^4 = $5167.27 ---------he's going to pay finally.

    Therefore, James will have to pay the $8000 he owed a total of (1000 +4000 +5167.27) = $10,167.27 in two years from today. ------------answer.

    ------------------------------------------------------------
    b) Use that formula?

    Let me pass.
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  3. #3
    MHF Contributor
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    Quote Originally Posted by julie View Post
    James borrowed $5,000 from his friend 2 years ago; and, an additional $3,000 1 year ago. He wants to repay his friend the money that he borrowed plus interest at 8% compounded quarterly.


    b) Calculate James' payments if he wants to fully repay his debt with two equal payments - the first 9 months from now & the second 18 months from now.

    Possible formula: Fv=PMT[ (1+i)^n -1 / i ]

    Someone please help me with this question...
    Thanks in advance
    That formula is not applicable to the problem, I'm afraid.
    Let me do it analytically.

    Let us say N = amount of equal payments each.

    After 9 months from today:
    The $5000 loan is [2 +(9/12)] = 2.75 years old, so, n1 = 2.75*4 = 11 compoundings
    The $3000 loan is 1.75 years old, so, n2 = 1.75*4 = 7 compoundings
    So his total debt 9 months from now is
    A(9) = 5000(1.02)^11 +3000(1.02)^7 = $9662.93
    Paying N,
    Balance = 9662.93 -N -----------**

    ---------------------
    After 18 months from today.
    That is 9 months from 9 months from today.
    So,
    P = 9662.93 -N
    i = 0.02
    n = (9/12)*4 = 3 compoundings

    New debt = (9662.93 -N)(1.02)^3
    That is equal to N, for his second and last equal payment.
    So,
    (9662.93 -N)(1.02)^3 = N
    We just isolate N and we're done.
    9662.93 -N = N /(1.02^3)
    9662.93 = N +[N /(1.02^3)]
    9662.93 = N[1 +1/(1.02^3)]
    9662.93 = N(1.942322335)
    N = 9662.93 / 1.942322335 = 4974.94

    Therefore, here, James has to pay $4974.94 twice to fully pay his debts is 18 months. -----------answer.
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  4. #4
    Newbie
    Joined
    Feb 2007
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    thnx

    Thank you so much, i was completley lost on this question even though it seems simple now. Again thanks!
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