Question

C&D stereo sold a stereo system on a plan that required no down payment and nothing to pay until January 1 (four months away). then the first of 12 monthly payments of $226.51 must be made. The payments were calculated to provide C&D Stereo with a return on the account receivable of 16.5% compounded monthly. what was the selling price of the stereo system?

Answer 1

To calculate the selling price of the stereo system, we use the present value of an annuity formula that accounts for the monthly payment, interest rate, and number of payments. This determines what the future monthly payments are worth in today's dollars, revealing the original cost of the stereo system.

Step-by-step explanation:

To find the selling price of the stereo system, we need to understand the concept of the present value of an annuity. An annuity is a series of equal payments made at equal intervals, and the present value is what those future payments are worth right now. In this scenario, each payment is $226.51, and there are 12 payments in total. The interest rate is 16.5%, compounded monthly. The formula to calculate the present value (PV) of an annuity is:

PV = Pmt × [(1 - (1 + r)^(-n)) / r]

Where Pmt is the monthly payment, r is the monthly interest rate (annual rate divided by 12), and n is the total number of payments.

Substituting the given values:

1. r = 16.5% / 12 = 0.1375
2. n = 12 months
3. Pmt = $226.51

Using these values, we can calculate the present value which will be the selling price of the stereo.

Thus, the selling price of the stereo system, when calculated using the above formula, gives us the cost of the stereo system as $226.51 multiplied by the present value interest factor for an annuity (PVIFA).