Question

The price of the used car is $23,500. Sales tax on this car is 7% of the price of the vehicle. You intend to finance the entire cost of the car and sales tax, less a down payment of $1,200. You intend to finance the car for 48 months and your car payment will be $551.44 per month.

What is the interest rate and how is it determined?

Answer 1

Computation of Loan Amount:
Price of Used Car	$         23,500
Sales Tax ($23,500 * 7%)	$           1,645
Total Cost	$         25,145
Less: Down Payment	$           1,200
Loan Amount	$         23,945
Monthly Payment =	$         551.44
No. of Payments =	48

Let 'i' be the rate of interest.

Loan Amount = PV of Monthly Installments

$23,945 = $551.44 * PVAF(i%,48 Months)

Let us assume i = 5%, Then

PV of Monthly Installments = $551.44 * PVAF((5/12)%,48 Months)

r = 5%/12	1+r	(1+r)^-n	1- [(1+r)^-n]	[1- [(1+r)^-n]] /r
0.42%	1.0042	0.8194	0.1806	43.4309

PV of Monthly Installments = $551.44 * 43.4160

PV of Monthly Installments = $23,941.32

As the PV of Monthly Installments approximately equal toLoa Amount, IRR = 5%