To solve this problem using a financial calculator, you need to identify each of the variables based on the information given. Here’s how to set it up:
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N (Number of periods): Since payments are made every six months for 28 years, you need to convert the years into semiannual periods. \[ N = 28 \text{ years} \times 2 = 56 \text{ periods} \]
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i.y (Interest rate per period): The annual interest rate is 14%, but since the payments are semiannual, you divide this by 2. \[ i.y = \frac{14%}{2} = 7% \text{ or } 0.07 \]
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PMT (Payment per period): This is the payment you receive every six months. \[ PMT = 3,593.00 \]
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PV (Present Value): This is what we are trying to find, the value today of the cash flows.
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FV (Future Value): For an annuity, this is typically 0 unless stated otherwise. Since the question is asking for the value today of the payments, you can use: \[ FV = 0 \]
With these values, you can input them into the financial calculator as follows:
- N = 56
- i.y = 7% (or 0.07 depending on the calculator)
- PMT = 3,593.00
- FV = 0
- PV = ? (this is what you will calculate)
Now, use the financial calculator to compute for PV. Make sure you set it to calculate present value of an annuity, which is typically the function used for this type of problem. The result will give you the present value of the money machine.
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