Final answer:
To calculate the required donation to account for inflation, you need to find the present value of the future payments using an interest rate of 8% per year. The formula for present value is PV = FV / (1 + r)^n, where PV is the present value, FV is the future value, r is the interest rate, and n is the number of years. In this case, the required donation is $375,000.
Step-by-step explanation:
To calculate the present value of future payments, we need to consider the concept of present discounted value. This is the amount we would need in the present to equal a certain amount in the future, taking into account an interest rate. In this case, the required donation for the annual $30,000 graduation party can be calculated by finding the present value of the future payments using an interest rate of 8% per year. The calculation can be done using the present value formula:
PV = FV / (1 + r)^n
Where PV is the present value, FV is the future value (in this case, $30,000), r is the interest rate (8% per year), and n is the number of years (which is infinity in this case as the party's cost will rise by 4% per year thereafter).
Using the formula with the given values:
PV = $30,000 / (1 + 0.08)^∞
Since the number of years is infinite, we can use the formula for the present value of a perpetuity which is:
PV = C / r
Where C is the cash flow per period (in this case, $30,000 per year) and r is the interest rate (8% per year).
Substituting the values into the formula:
PV = $30,000 / 0.08 = $375,000
Therefore, you need to donate $375,000 now to account for the effect of inflation and ensure the future payments cover the increased cost of the party.