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

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 2

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

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.