finite math

using the formula for present value of ordinary annuity or the amortization formula to solve this problem.

PV=13000
I= .015
PMT=550
n?

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asked by carol
  1. Is I the annual interest or monthly interest?
    It will be assumed monthly interest.

    Present Value, P = 13000
    Payment (monthly) A = 550
    interest (monthly) i = 0.015

    The amortization formula would equate future value with the sum of all the payments, all increased at rate of interest i.

    Future value = sum of all payments

    Let R=1+i
    PRn = A + AR + AR² + AR³ + ... + ARn-1
    =A(Rn+1)/(R-1) (by factoring)
    Hence
    (Rn-1)/((R-1)*Rn) = P/A

    To solve for the period n, there is no explicit formula to calculate.

    The easiest way is to calculate the payment for a given period n.

    If the payment matches 550, then the estimated n is correct.

    For example,

    The equation can be converted into a formula for the monthly payment, A

    A=P(R-1)R^n/(R^n-1)
    For
    P=13000
    R=1.015
    we make a first estimate from
    13000/550=23.6
    We know n>23.6, so try 30
    A=13000(.015)1.015^30/(1.015^30-1)
    =541.3 < 550
    So we try 29 payments
    A=556.1
    We then know that the period n lies between 29 and 30, and for all practical purposes, we would put it at 30.

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  2. The right-hand side of the amortization formula should read:

    A(Rn-1)/(R-1) (by factoring)

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