SOLUTION: Please help me with this, thank-you. Installment plant mike's sporting goods sell elliptical trainers under under 2 payment plans cash or installment under the installment plan the

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Question 1178748: Please help me with this, thank-you. Installment plant mike's sporting goods sell elliptical trainers under under 2 payment plans cash or installment under the installment plan the customer pays $22/month over 3 years with interest charged on the balance at rate of 18%per year compounded monthly.find cash price for an elliptical trainer if it is equivalent to the price paid by a customer using the installment plan answer
Answer by CPhill(1959) (Show Source):
You can put this solution on YOUR website!
Let's break down how to find the equivalent cash price of the elliptical trainer.
**1. Calculate the Total Number of Payments:**
* The customer pays $22 per month for 3 years.
* Total payments: 3 years * 12 months/year = 36 payments
**2. Calculate the Monthly Interest Rate:**
* The annual interest rate is 18%.
* The monthly interest rate is 18% / 12 = 1.5% = 0.015.
**3. Use the Present Value of an Ordinary Annuity Formula:**
* The cash price is equivalent to the present value of the installment payments.
* The formula is: PV = PMT * [1 - (1 + r)^-n] / r
Where:
* PV = Present Value (cash price)
* PMT = Monthly payment ($22)
* r = Monthly interest rate (0.015)
* n = Number of payments (36)
**4. Plug in the Values and Calculate:**
* PV = 22 * [1 - (1 + 0.015)^-36] / 0.015
* PV = 22 * [1 - (1.015)^-36] / 0.015
* PV = 22 * [1 - 0.580039] / 0.015
* PV = 22 * [0.419961] / 0.015
* PV = 22 * 27.9974
* PV ≈ $615.94
**Therefore, the cash price for the elliptical trainer is approximately $615.94.**