Question

What is the value today of a money machine that will pay $500.00 every 6 months for 30.00 years? Assume the first payment is made six months from today and the interest rate is 7.00%.

Answer 1

what values do I enter for N, i/y, PV, PMT, and FV to solve on a finance calculator?

Answer 2

To calculate the present value of a series of cash flows from a money machine that pays $500 every 6 months for 30 years at an interest rate of 7% compounded semi-annually, we can use the present value of an annuity formula.

**Given:**
- Payment (PMT) = $500
- Interest Rate (i) = 7% per year = 3.5% per 6 months = 0.035
- Number of Periods (n) = 30 years * 2 = 60 periods

The present value of an annuity formula is:

\[
PV = PMT \times \left(1 - (1 + i)^{-n}\right) / i
\]

Plugging in the values:

1. **PMT = $500**
2. **i = 0.035**
3. **n = 60**

Now, substitute these values into the formula:

\[
PV = 500 \times \left(1 - (1 + 0.035)^{-60}\right) / 0.035
\]

Let's calculate the components:

1. Calculate \( (1 + 0.035)^{-60} \):

\[
(1 + 0.035)^{-60} = (1.035)^{-60} \approx 0.2151
\]

2. Substitute back into the annuity formula:

\[
PV = 500 \times \left(1 - 0.2151\right) / 0.035
\]

Calculate \( 1 - 0.2151 \):

\[
1 - 0.2151 \approx 0.7849
\]

Now substitute this into the formula:

\[
PV = 500 \times 0.7849 / 0.035
\]

Calculate \( 784.9 / 0.035\):

\[
PV = 500 \times 22413.67 \approx 11206.84
\]

Thus, the present value of the money machine that pays $500 every 6 months for 30 years at a 7% interest rate is approximately **$11206.84**.

Answer 3

To solve for the present value of the annuity (the money machine paying you $500 every 6 months for 30 years) using a financial calculator, you'll typically enter the following values:

- **N (Number of periods)**: This represents the total number of payment periods. Since the payment is made every 6 months for 30 years, you would calculate:
\[
N = 30 \text{ years} \times 2 \text{ payments per year} = 60
\]

- **I/Y (Interest rate per period)**: This is the interest rate per period. Since the annual interest rate is 7%, and payments are made every 6 months, you divide by 2:
\[
I/Y = \frac{7\%}{2} = 3.5
\]

- **PV (Present Value)**: This is the value you are solving for, so you initially leave this blank or enter 0 if your calculator requires you to input all fields.

- **PMT (Payment)**: This is the amount of each periodic payment. For this scenario, it is:
\[
PMT = 500
\]

- **FV (Future Value)**: Since the annuity does not have a future value to consider at the end of the payment periods (for this type of calculation), you can enter:
\[
FV = 0
\]

**Summary of Values to Enter:**

- **N = 60**
- **I/Y = 3.5**
- **PV = 0** (you will calculate this)
- **PMT = 500**
- **FV = 0**

After entering these values into your financial calculator, you will compute for PV (the present value), which should return the present value based on the annuity payments specified.