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 n specifies 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 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 = Ai, 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.