Question

A store finances a vehicle in 48 monthly installments of $499.00 at a rate of 18% per year Calculate the initial value of the vehicle

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Corbin

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To calculate the initial value of the vehicle, we need to find the present value of the 48 monthly payments of $499.00 each at an annual interest rate of 18%.

Using the formula for the present value of an ordinary annuity:

PV = PMT \times \left( \frac{1 - (1 + r)^{-n}}{r} \right)

where:

PV = present value,

PMT = monthly payment,

r = monthly interest rate,

n = number of periods.

Given:

PMT = ,

r = \frac{18\%}{12} = 0.18/12 = 0.015 (monthly interest rate),

n = 48 (number of payments).

Substitute the given values into the formula:

PV=499\times\left(\frac{1-\left(1+0.015\right)^{-48}}{0.015}\right)

PV\approx16987.23

Answer: $16987.23

Using the formula for the present value of an ordinary annuity:

where:

Given:

Substitute the given values into the formula:

Answer: $16987.23

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