Posted by **Ajax** on Monday, December 21, 2009 at 3:38pm.

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 -
**Ajax**, Monday, December 21, 2009 at 6:35pm
Please respond somebody!!!

- math: precalc -
**Reiny**, Monday, December 21, 2009 at 6:40pm
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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