math: precalc
posted by Ajax on .
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 onesixtieth 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.

Please respond somebody!!!

16000 = 300(1  (1+i)^60)/i
53.3333 = (1  (1+i)^60)/i
After a few trialanderror 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) = (53.333353.24886)/(53.56153.24886)
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%