You have found a car at a car lot and in typical fashion are invited into the of

Question

You have found a car at a car lot and in typical fashion are invited into the office to "work a deal". You know the price of the car is $10,000 (which is what you need to borrow) and the term is 60 months. The salesperson does not tell you the interest rate, but instead says he/she can get you a payment of $199/month. What annual interest rate are you being offered in this loan scenario?

Round to the nearest whole number and entire your answer as a whole number. For example, if the answer is 12%, enter 12 in the answer box. Please use an Excel formula for the most accurate answer. Assume

your first loan payment is due at the end of the month.

Explanation / Answer

We need to use the following formula:

Present Value = Monthly Fixed Payment x Present Value Interest Factor (r%, 60 months)

Where r is the monthly interest rate we need to find.

Here:

$10,000 = $199 x Present Value Interest Factor (r%, 60 months)

Or, Present Value Interest Factor (r%, 60 months) = $10,000 / $199 = 50.2513

Present Value Interest Factor (r%, 60 months) = [1 - (1+r) -60] / r = 50.2513

Or, [1 - (1+r) -60] = 50.2513 x r

Solving for r in excel, the nearest integer value for r = 0.55%

Or, annual interest rate = 0.55% x 12 = 6.6% = 7% (closest integer)

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