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Math Help - Interest Rate and principal calculations

  1. #1
    Ife
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    Interest Rate and principal calculations

    Can i get some guidance with this calculation please??

    At the start of the month, a customer owes a credit card company $1000. In the middle of the month, the customer pays $P to the company, where P< $1000.
    At the end of the month, the company adds interest at the rate, R, of 3% of the amount still owing. This procedure is repeated in each subsequent month.

    a. Find the value of P for which the customer owes $1000 at the end of every month.

    b. Find the value of P, for which the whole amount is paid off after the second payment.

    c. Assuming that the debt is not paid off after 4 payments, show that the amount still owing at the beginning of the 5th month can be expressed as

    $ (1000R^4 - (PR(R^4-1))/R-1 ), R=1.03

    d. Show that the value of P for which the whole amount owing is exactly paid off after the nth payment is given by

    P = (1000R^n-1 (R-1) ) / (R^n - 1)
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  2. #2
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    A.
    (1000-P)*(1+.015)=1000
    =1015-P(1.015)=1000
    =P(1.015)=15
    P=14.78

    This assumes that r is the montly interest rate. If that is the annual intererst rate then you would divide r by 12.

    B.
    (1000-P)*(1+.015)=P
    =1015-P(1.0150=P
    1015=P+1.015*p
    1015=P(1+1.015)
    P=503.72

    Use this same logic to solve the following problems. I hope this helps.
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  3. #3
    MHF Contributor
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    Quote Originally Posted by Ife View Post
    At the end of the month, the company adds interest at the rate, R, of 3% of the amount still owing.
    You better check that...seems to mean there is no charge for the
    1st half of the month, where the amount owing is different...
    Like, there MUST be a charge on the $1000 owing up to midmonth; no?
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