Your child's orthodontist offers you two alternative payment plans.The first plan requires a $3,500 immediate up-front payment.The second plan requires you to make monthly payments of $137.41,payable at the end of each month for 3 years.What nominal annual interest rate is built into the monthly payment plan?

Question

Quizplus · Accepted Answer

To find the nominal annual interest rate, we need to first determine the total amount paid under the second plan:

Total payment = monthly payment x number of payments
Total payment = $137.41 x 36 (3 years x 12 months per year)
Total payment = $4,945.56

The nominal interest rate can be found by solving for "i" in the following equation:

Present value = payment x ((1 - (1 + i)^-n)/i)

Where:
- Present value = $3,500 (the amount paid up-front)
- Payment = $137.41
- n = 36 (number of monthly payments)

Using a financial calculator or spreadsheet, we find that the nominal interest rate built into the payment plan is 24.05%.

Therefore, the best choice is C, which corresponds to 24.05%.

Your Child's Orthodontist Offers You Two Alternative Payment Plans