BONUS! 3 pts You have your eyes on a new automobile costing $30,000. If you had the $30K and wrote a check for that amount, you could drive the car home. However….you don’t have it, so you pay $5000 down and finance $25,000 through the dealer at a rate of 6% compounded monthly. The dealer requires monthly payments over 5 years. The dealer then proceeds to add on a 1.25% loan initiation fee of $250. Also, they have a prepaid loan closeout fee of another $250. Then, there is another paperwork filing and storage fee of another $100, and a prepaid load maintenance fee of only’ $8/mo, or $480. At this point, the salesman is talking very fast and assures you that these small ‘required’ amounts can be rolled into your loan. They figure your monthly payment as A = $26,080(A/P 112, 60) = $504.13 a) b) What is the effective monthly rate of interest you are really paying for this loan? What is the nominal annual rate? c) What is the effective annual interest rate you are really paying?
(A/P, i, N) = Capital Recovery Factor = [i * (i + 1)^N] / [(1 + i)^N – 1]
$504.13 = $26,080 * [i * (i + 1)^N] / [(1 + i)^N – 1]
By using calculator we find that i ~= 13%
Effective Interest rate = 13%
Nominal Interest rate = 6%