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.
