Judy has $2,000 for a down payment on a vehicle, and she can afford monthly payments of $400. If lenders are currently offering 6% interest on 5-year loans, what is the maximum price Judy can pay for a vehicle?

Present value of her affordable value

= 400(1 - 1.005^-60)/.005
= ...

Don't forget to add the $2000 downpayment she already has

To find the maximum price Judy can pay for a vehicle, we need to consider the down payment, monthly payments, and the interest rate.

First, let's calculate the total amount Judy can borrow for the vehicle.

Using the formula for the present value of an ordinary annuity, we can determine the loan amount.

The present value of an ordinary annuity formula is:

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

Where:
PV = Present Value (loan amount)
PMT = Monthly Payment
r = Interest Rate per Period
n = Number of Periods

In this case, Judy can afford monthly payments of $400, and lenders are offering a 6% interest rate on 5-year loans.

Converting the interest rate to a decimal form: 6% = 0.06

Now we can calculate the present value (loan amount):

PV = $400 x (1 - (1 + 0.06)^(-5)) / 0.06

PV = $400 x (1 - (1.06)^(-5)) / 0.06

PV ≈ $400 x (1 - 0.7473) / 0.06

PV ≈ $400 x (0.2527) / 0.06

PV ≈ $1,684.50

So, the maximum loan amount Judy can borrow is approximately $1,684.50.

To determine the maximum price Judy can pay for a vehicle, we need to add the down payment to the loan amount:

Maximum price = down payment + loan amount

Maximum price = $2,000 + $1,684.50

Maximum price ≈ $3,684.50

Therefore, the maximum price Judy can pay for a vehicle is approximately $3,684.50.

To find the maximum price Judy can pay for a vehicle, we need to consider her down payment, monthly payments, and the interest rate offered by the lenders.

First, let's calculate the total amount that Judy can afford to borrow over 5 years (60 months). She can afford monthly payments of $400, so multiplying that by the number of months gives us:

$400 * 60 = $24,000

Now, let's calculate how much Judy will have to repay, including the interest. The interest rate is 6%, so we need to add it to 100% to account for the principal amount (loan amount) and the interest. Therefore, the interest rate as a decimal is 1 + 0.06 = 1.06.

Now, we can use the future value of an ordinary annuity formula to calculate the loan amount Judy can afford based on her monthly payments:

Loan Amount = Monthly Payment * ((1 - (1 / (1 + Monthly Interest Rate)^Number of Payments)) / Monthly Interest Rate)

The monthly interest rate is 6% divided by 12 (number of months in a year):

Monthly Interest Rate = 6% / 12 = 0.005

Now, we can plug in the values and calculate the loan amount:

Loan Amount = $400 * ((1 - (1 / (1 + 0.005)^60)) / 0.005)

Using a financial calculator or spreadsheet software, we can find that the loan amount Judy can afford is approximately $23,871.74.

Lastly, we need to subtract Judy's down payment from the maximum loan amount to find the maximum price she can pay for a vehicle:

Max Price = Loan Amount + Down Payment

Max Price = $23,871.74 + $2,000 = $25,871.74

Therefore, the maximum price Judy can pay for a vehicle is approximately $25,871.74.