Question

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%.

Answer 1

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.