Davis is buying a new car for $21,349.00. He plans to make a down payment of $3,000.00. If he's to make monthly payments of $352 for the next 5 years what APR had he paid

He actually borrowed P=21349-3000=18349 (present value)

Assume the monthly interest is i.

then future value due to loan:

F1=P (1+i) ^n=18349 (1+i) ^ (5*12) = 18349 (1+i) ^60

future value from monthly payment of A=352

F2=A ((1+i) ^n-1) / i=352 ((1+i) ^60-1) / i

Since F1=F2 for the same loan, we have

18349 (1+i) ^60=352 ((1+i) ^60-1) / i

Simplify notation by defining R=1+i, then

18349 (R^60) - 352 (R^60-1) / (R-1) = 0

Simplify further by multiplication by (R-1)

f (R) = 18349*R^60 * (R-1) - 352 (R^60-1) = 0

Solve for R by trial and error, or by iteration to get R=1.004732

The APR is therefore

12 * (1.004732-1) = 0.056784, or 5.678% approx.