Interest Rate Question?

Question

Suppose that Braun runs an ad for a Escalade that says “Zero down, 0% financing, $799 per month for five years, or buy for $43,599. Is this really 0% financing? Explain.

If not, find the approximate annual interest rate, compounded monthly. Can anyone help me with this?

Answer 1

799*60 = 47,940 ≠ 43,599
So, there is a finance charge. Given that you want the equivalent annual rate under the assumption of monthly compounding, you want to know the rate of interest i that satisfies the equation:

43,599 = 799(1+i)^(1/12) + 799(1+i)^(2/12) + 799(1+i)^(3/12) + ... + 799(1+i)^(60/12)

This presumes your payments are due at the end of the month. Thus,

43,599 = 799[(1+i)^(1/12) + (1+i)^(2/12) + (1+i)^(3/12) + ... + (1+i)^(60/12) ]
54.567 = (1+i)^(1/12) + (1+i)^(2/12) + (1+i)^(3/12) + ... + (1+i)^(60/12)
54.567 = [1 – (1+i)^(-60/12)]/[(1+i)^(1/12) – 1]
54.567 = [1 - (1+i)^(-5)]/[(1+i)^(1/12) – 1]

i = .03866 (approximately 3.866%)

Answer 2

$799 /month for 5 years is: $47,940
Subtracting instant price of $43,599
leaves a balance of $4,341 almost 10%
You'd have to check interest tables for rate.