# math: precalc

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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 -

• 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

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

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