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March 28, 2017

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You are going to buy a $18,000 car. The dealer offers you $2000 cash back of nothing down and 0% financing for 60 months. If you take the financing, starting in one month you will pay one-sixtieth of $18,000 each month for 60 months. In some sense that is not really "0% financing" because you could have bought the care for, effectively, $16,000 and you will be making $18,000 in payments. Use the present value formula to determine the actual finance rate. [Hint: Do not expect to solve it algebraically.]

Present value Formula: A={R[1-(1+i)^-n]} / i

where A is the present value, R is the amount of each payment, i is the rate per time period, and n is the time period.

  • math: precalc - ,

    Please respond somebody!!!

  • math: precalc - ,

    16000 = 300(1 - (1+i)^-60)/i
    53.3333 = (1 - (1+i)^-60)/i

    After a few trial-and-error attempts with my calculator, I "sandwiched" the rate i between .004 and .0038

    so
    .004 53.24886
    i 53.33333
    .0038 53.561
    we can now set up an interpolation ratio
    (i - .004)/(.0038 - .004) = (53.3333-53.24886)/(53.561-53.24886)
    i = .003946

    check:
    300(1 - (1.003946)^-60)/.003946 = 15999.86
    not bad

    so the annual rate is approx .003946 x 12 = .04735
    or 4.735%

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