APR Homework

1) Calculate the APR of the following add-on loans assuming monthly
payments (exactly like you did in Friday lab, so pull out your notes from
Friday). Recall that for the arithmetic series (sum), S=1+2+3+ … +n, we
n(n  1)
showed on Friday that S 
.
2
a. Purchase a living room set for $3600 with a 7.5% add-on loan over a
3 year period.
b. Purchase a stereo set for $2760 with a 7.5% add-on loan over a 3 year
period.
2) Did the principal mater in the above calculation? Justify your answer by
calculating the APR for a 7.5% 3 year add-on loan for $P. Hint: It may be
easier to think of the principal in terms of the monthly payment, d; let P=36d
where d represents the monthly payments towards the loan balance and then
show that the value of d is irrelevant in the calculation of this APR.
3) Determine the general form of the APR of an add-on loan. In other words,
what is the APR of an add-on loan for $P with N total payments made n
times per year at a rate of r? I think it would be helpful to let P=Nd, as you
2rt
did with #2. You should get a compound period rate of i 
, so
N 1
 2rt  2rnt
2rN
2rN
APR  ni  n

. Note that since APR 
, the

N  1 N  1 N  1
N 1
only thing relevant when determining APR is the
 add-on rate and the totally
number of payments (so the principal and the actual loan time are
irrelevant).

4) A car dealer will sell you the $18,436 car of your dreams for $3,000 down
and 60 easy monthly payments of $384.
a. How much would you end up paying for the car?
b. How much interest would you pay?
c. Assuming this is an add-on loan, what is the add-on interest rate?
d. Assuming this is an add-on loan, what is the APR? Note that you may
2rN
use the formula derived in #3 to answer this: APR 
.
N 1
