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 = ?.
Correction: P = 150 * 48 = $7200.
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.