Question

You are in the market for a new boat (pictured above) from John’s Marine. After trade in of your old boat, the purchase price of your new boat is $32,125. There are two options to pay for it. This can be financed by your local bank at 3.2% APR with payments over the next 4 years or you can get an additional $3,000 discount off the purchase price if you finance the loan with John’s Marine at an APR of 8.0% over the same 4-year period. Should you take the offer of 3.2% APR for 4 years from the local bank or the $3,000 rebate and 8.5% APR from John’s Marine? Both APRs are compounded monthly.

Answer 1

Purchase price of boat is $32,125

APRs are compounded monthly

Option 1	Option 2
Loan from local bank	Loan from John's Marine
Annual percentage rate (APR) = 3.2%	Annual percentage rate (APR) = 8.5%
Time = 4 years	Time = 4 years
	Discount = $3,000

Computation of amount paid for a new boat

Option 1:

Principal	$32,125
APR Per month	3.2/12=0.27%
Time in month	4*12 = 48 months
Amount paid	32,125(1+0.27/100)^48 = 32,125(100.27/100)^48 = 32,125(1.0027)^48 = 32,125 *1.1359 = $36,491

Option 2:

Principal	$32,125
APR Per month	8.5/12 = 0.71%
Time in month	4*12 = 48 months
Discount	$3,000
Net Principal	$32,125 - $3,000 = $29,125
Amount paid	29,125(1+0.71/100)^48 = 29,125(100.71/100)^48 = 29,125(1.0071)^48 = 29,125*1.3948 = $40,624

Conclusion:

Under option 1 amount paid is less than option 2 hence, option 2 is best choice.

I should take offer of 3.2% APR for 4 years

Note : under option 2 i.e. finance from John's Marine APR is considered as 8.5 %

I think in the question by mistake there are different APR is given for same option i.e finance from John's Marine 8% and 8.5%

Thank you :)