To determine the present value (PV) Derek would be willing to pay today instead of making monthly payments on the loan for the car, you can use the present value formula for an annuity, since he will be making equal monthly payments.
Here’s what you’ll need to input into a financial calculator:
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N (Number of Payments): This is the total number of monthly payments Derek will make. He will pay for 5 years, and since payments are monthly: \[ N = 5 \text{ years} \times 12 \text{ months/year} = 60 \text{ payments} \]
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PMT (Payment Amount): This is the amount Derek will pay each month. In this case, it is: \[ PMT = 547.00 \]
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i/y (Interest Rate per Period): Since the annual interest rate is 6%, and since the payments are monthly, you need to convert this into a monthly interest rate: \[ \text{Monthly interest rate} = \frac{6%}{12} = 0.5% = 0.005 \text{ (in decimal form)} \]
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FV (Future Value): Since we are considering the present value of the payments and not the future value, we can set this to 0. \[ FV = 0 \]
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PV (Present Value): This is what we are solving for; it represents the maximum amount Derek should be willing to pay today instead of making the payments.
Summary of Inputs:
- N: 60
- PMT: 547.00
- i/y: 0.5 (or 6% annually)
- FV: 0
Now you can use your financial calculator to calculate the present value (PV) with these inputs.
When you do this, you will find the maximum amount Derek should be willing to pay today for the car.
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