To solve this problem using a finance calculator, we need to determine the present value (PV) of an annuity due, since the first payment is made today. Here's how to set up the calculator:
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N (Number of Payments): Since the question states that there will be 9 total payments, and the first payment is made today, you will enter \(N = 9\).
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PMT (Payment per Period): The payment you receive each year is $8,099. Therefore, enter \(PMT = 8099\).
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i/y (Interest Rate per Period): The interest rate given is 15.00%. Therefore, enter \(i/y = 15\).
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FV (Future Value): The future value is not relevant for this calculation since we are only looking for the present value in this case, so you can leave this as \(FV = 0\) or input it as such if required by the calculator.
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PV (Present Value): This is what you are solving for in the calculation.
Since this is an annuity due, you need to adjust for the fact that payments are made at the beginning of each period. You can usually do this by calculating the present value of an ordinary annuity (where the first payment is at the end of the period) and then multiplying the result by \((1 + i/y)\) to account for the additional period.
After entering these values, you can compute \(PV\) on the finance calculator.
Summary of inputs:
- N = 9
- PMT = 8099
- i/y = 15
- FV = 0 (not needed for this calculation)
- PV = ? (calculate this to find the present value)
To find PV:
- Calculate the ordinary annuity due's present value.
- Multiply the result by \((1 + i/y)\).
Alternatively, some finance calculators have a function specifically for annuities due; you may need to check your calculator's manual for that feature.
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