# Jennifer bought a brand new treadmill on a credit plan at BeFit Exercise Equipment. BeFit will charge her 15% per year compounded monthly. If her monthly payments will be \$150 for 4 years, how much was the original price of the treadmill?

a) \$5,390.72
b) \$5,389.72
c) \$5,388.72
d) \$5,392.72
e) \$5,385.72

## P = Po(1+r)^n.

P = 4 * 150 = \$600.
r = 0.15/12mo. = 0.0125/mo.
n = 12Comp./yr. * 4yrs. = 48 Compounding periods.
Po = ?.

## To find the original price of the treadmill, we can use the formula for the present value of an ordinary annuity.

The formula is:

PV = PMT * ((1 - (1 + r)^(-n)) / r)

Where:
PV = Present value (original price of the treadmill)
PMT = Monthly payment (\$150)
r = Monthly interest rate (15% per year, compounded monthly, so 15% / 12 = 1.25% or 0.0125 as a decimal)
n = Number of payments (4 years * 12 months = 48 months)

Let's calculate the present value (original price):

PV = \$150 * ((1 - (1 + 0.0125)^(-48)) / 0.0125)

Using a calculator, we can simplify this calculation.

PV ≈ \$150 * ((1 - 0.607425745) / 0.0125)

PV ≈ \$150 * (0.392574255 / 0.0125)

PV ≈ \$150 * 31.4059404

PV ≈ \$4,711.91

Therefore, the original price of the treadmill was approximately \$4,711.91.

None of the given answer choices are correct.

## To find the original price of the treadmill, we need to calculate the present value of the monthly payments.

First, let's calculate the number of months in 4 years:
Number of Months = 4 years * 12 months/year = 48 months

Next, let's calculate the monthly interest rate:
Monthly Interest Rate = Annual Interest Rate / 12 = 15% / 12 = 0.15 / 12 = 0.0125

Now, let's use the formula for the present value of an annuity to calculate the original price of the treadmill:

Present Value = Monthly Payment * ((1 - (1 + r)^(-n)) / r)

where:
- Monthly Payment = \$150
- r = monthly interest rate = 0.0125
- n = number of months = 48

Substituting these values into the formula, we have:

Present Value = \$150 * ((1 - (1 + 0.0125)^(-48)) / 0.0125)

Using a calculator, we find that the Present Value is approximately \$5,388.72.

Therefore, the original price of the treadmill was \$5,388.72.

The correct answer is c) \$5,388.72.