Richard purchased a car for $39,905. He made a downpayment of $15,000 and paid $614 monthly for 4 years. Find the APR.

Question

Richard was able to payoff the loan at the end of 30 months. Using the Actuarial method find he unearned interest, and payoff amount

Answer 1

let the monthly rate be i
614( 1 - (1+i)^-48)/i = 24905
(1 - (1+i)^-48)/i = 40.56189

that's toughie to solve, I will use Wolfram
https://www.wolframalpha.com/input/?i=solve+614(+1+-+(1%2Bx)%5E-48)%2Fx+%3D+24905

i = .00709
so the annual rate compounded monthly
= 12(.00709) = appr.085 or 8.5%

for the second part, I am not familiar with US actuarial methods