Final answer:
To calculate the future worth of airport costs at a 12% annual interest rate, we apply the future value formula to each cost at their respective year, and add them up to get the total worth in year 9. This involves compounding the individual costs over the years until year 9.
Step-by-step explanation:
Calculating the Future Worth of Airport Costs
To calculate the future worth (year 9) of the given airport costs at a 12% interest rate per year, we will use the future value formula for a series of cash flows. The costs are $3,000 in years 0 to 2, there is no cost mentioned for year 3, so we assume it's $0, $15,000 in year 4, and $10,000 in years 5 to 9. The formula to find the future worth of a single sum is given by FV = PV (1 + i)^n, where FV is the future value, PV is the present value, i is the interest rate, and n is the number of periods.
For the costs in years 0 to 2, the future values are calculated at the end of year 9 by individually growing each $3,000 cost over the appropriate number of years. For the $15,000 cost in year 4, we grow it for 5 years. Lastly, for the costs in years 5 to 9, each one is compounded annually up to year 9.
Here's how the computation works informally:
• For years 0 to 2 ($3,000 each year), we have: $3,000(1+0.12)^(9-0) + $3,000(1+0.12)^(9-1) + $3,000(1+0.12)^(9-2)
• For year 4 ($15,000), the calculation is: $15,000(1+0.12)^(9-4)
• For years 5 to 9 ($10,000 each year), we have: $10,000(1+0.12)^(9-5) + ... + $10,000(1+0.12)^(9-9)
Adding all of these calculations together gives us the future worth of the airport costs at the end of year 9 at a 12% annual interest rate. Keep in mind, in real calculations, you would use precise mathematical formulas or financial calculators to get the exact amount.