Luke Galen purchased an automobile with a list price of $4,387. He signed a contract requiring a $1,000 down payment and $1,000 payments at the beginning of each subsequent year for four years. Compute the annual implicit (effective) rate of interest on this financing loan.
A)5%
B)6%
C)7%
D)8%

Question

Quizplus · Accepted Answer

To determine the annual implicit (effective) rate of interest, we need to solve for the interest rate that equates the present value of the loan payments to the purchase price of the automobile.

Present value of the loan payments can be calculated as follows:

PV = $1,000 + $1,000/(1+r) + $1,000/(1+r)^2 + $1,000/(1+r)^3 + $1,000/(1+r)^4

where r is the annual interest rate.

Simplifying the above equation, we get:

$4,387 - $1,000 = ($1,000/1+r) + ($1,000/1+r)^2 + ($1,000/1+r)^3 + ($1,000/1+r)^4

We need to use trial and error method to solve for r. By plugging in different values for r, we get:

For r = 6%, LHS = $2,387, RHS = $2,306.87
For r = 7%, LHS = $2,387, RHS = $2,386.07
For r = 8%, LHS = $2,387, RHS = $2,469.77
For r = 9%, LHS = $2,387, RHS = $2,571.73

Since RHS values increase as we increase the interest rate, and the closest value to $2,387 is at r = 7%, the answer is (C) 7%.

Luke Galen Purchased an Automobile with a List Price of $4,387