Calculating Future and Present Values

You will need to complete each problem listed below. Each question is worth 10 points each for a total value of 50 points for the entire assignment.

Discounting Formula for Present Value: PV = FV/(1+i)n

Compounding Formula for Future Value: FV= PV(1+i)n

Note: When dealing with interest that is compounded in a different time period other than years, you will need to divide the interest rate by the number of periods and be sure that nspecifies the correct time frame. For example, if interest is compounded monthly over a three year timeframe, then you will need to divide the interest rate by 12 to reflect a monthly interest rate and express n as 36 months (3 years x 12 months) instead of 3 years.

You can also refer to your recommended textbook: Fundamentals of Financial Management Concise 8th Edition by Eugene Brigham and Joel Houston on pages 165-167 for additional examples of this.

1. Pastureland in the Brazos County is selling for $3,000 per acre. If the value increases 4% per year, what will the value be in 20 years?

2. Rebecca Smith just graduated from college and received a job managing a ranch. Her salary will be $25,000 per year. If she is guaranteed a 5% raise each year, what will her salary be in 23 years?

3. If you could buy a bond now and five years later sell it for $40,000, what would you be willing to buy it for, assuming an 8% discount rate and no other cash flows?

4. Twenty years ago, your grandfather deposited $800 in a savings account earning 5% annually, with interest compounded on a quarterly basis. What is that savings account worth today? What would the savings account be worth if interest were compounded monthly?

5. You have just struck oil in the middle of your hay field. An oil company has offered to pay you a perpetual annuity of $12,500 per year for the rights. The value of the offered annuity, assuming a 10% discount rate is calculated using the following formula: V0 = , where V0 is the future value of the series of payments, A is the present value of the annuity, and i is the interest rate.

V0 = 12,500/0.10 = $125,000

What would be the value of the annuity in question if the company increased the payment by 3% each year to for inflation? You will need to calculate the real interest rate by using the following formula: i* = [(1 + i) / (1 + I)] 1

Where the real (growth) rate = i*, nominal (growth) rate = i, and where I = inflation rate.

After calculating the real interest rate, use the present value of the annuity formula listed above determine the new value of the annuity.