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What values do I enter for N, PMT, i/y, FV and PV on a finance calculator to solve for the question below.

What is the value today of a money machine that will pay $4,497.00 per year for 29.00 years? Assume the first payment is made 8.00 years from today and the interest rate is 11.00%.

1 answer

To solve this problem using a financial calculator, first, you need to determine the present value of the cash flows generated by the money machine. Since the first payment happens 8 years from today, we will first calculate the present value of the annuity as of year 8, and then we will discount that amount back to today (year 0).

Step 1: Calculate the Present Value of the Annuity at Year 8

  1. N (Number of Payments): Since the annuity pays $4,497.00 per year for 29 years: \[ N = 29 \]

  2. PMT (Payment): Annual payment to be received: \[ PMT = 4,497.00 \]

  3. i/y (Interest Rate): Annual interest rate expressed as a percentage: \[ i/y = 11% \]

  4. FV (Future Value): Since we're dealing with an annuity, we set FV to 0: \[ FV = 0 \]

  5. PV (Present Value): This is what we are trying to find for the annuity at year 8.

Calculate PV at Year 8

Using these values, you would find the present value of the annuity at year 8, which is: \[ PV_8 = ? \] After entering the values into your calculator, compute the present value (PV at year 8).

Step 2: Discount the Value from Year 8 to Year 0 (Today)

Once you have the present value of the annuity at year 8, you need to discount it back to year 0 (today) because:

  1. N (Number of Compounding Periods): Since the first payment starts at year 8 and you're calculating back to today (year 0): \[ N = 8 \]

  2. PV (Present Value): You have just calculated this from the annuity in the previous step.

  3. PMT: Set it to 0 because you are not receiving any additional payments at this calculation stage.

  4. FV: This will be the present value calculated previously: \[ FV = PV_8 \text{ (the value you computed in Step 1)} \]

  5. i/y: This remains the same: \[ i/y = 11% \]

Final Calculation:

Now, you'll discount the calculated \( PV_8 \) back to today using the calculator with these values to find the present value (PV) at year 0.

In summary into two calculations:

  • First Calculate PV at Year 8 with \( N=29, PMT=4497, i/y=11, FV=0 \).
  • Then Use the result of \( PV_8 \) to calculate present value at Year 0 with \( N=8, FV=PV_8, PMT=0, i/y=11 \).

This will give you the value today of the money machine.