Craig has just been quoted what appears to be a very competitive loan for $3,500 to be paid back in 36 monthly payments of $123.47 and a finance charge of $945.However,the lender said that the interest would be calculated using the add-on method.Using the n-ratio method of estimating the APR,what is the APR on this loan?
$ \mathrm{APR}=\frac{\mathrm{Y}(95 \mathrm{P}+9) \mathrm{F}}{12 \mathrm{P}(\mathrm{P}+1)(4 \mathrm{D}+\mathrm{F})} $

Question

Quizplus · Accepted Answer

Using the add-on method, the total amount to be paid back is $3,500 + $945 = $4,445. Therefore, the monthly interest can be calculated as ($4,445 - $3,500)/36 = $26.25.
Using the n-ratio method, we have:
P = 36 (number of payments)
D = $123.47 (monthly payment)
F = $945 (finance charge)
N = 95 (number of days in loan term)
R = 365 (number of days in year)
Y = 1 (since payments are monthly)
Using the formula, we get:
APR = (1 x (95 x 12 + 9) x $945) / (12 x 36 x (36 + 1) x (4 x $123.47 + $945)) = 16.3%
Therefore, the APR on this loan is 16.3%, which is closest to option B (16.3%). Option A (14.9%) and D (13.2%) are lower, while option C (9.0%) is much lower and therefore not a valid choice.

Craig Has Just Been Quoted What Appears to Be a Very