Final answer:
The present value of the saving cash flow is approximately $1,233,108.75 when the first deposit is made at the end of the year, and approximately $1,347,732.42 when the first deposit is made at the beginning of the year. AAA does not have enough money to build the resort as the present value of the saving cash flow is lower than the total cost of $5,000,000.
Step-by-step explanation:
To calculate the present value of a future cash flow, we use the formula:
Present Value = Cash Flow / (1 + Interest Rate) ^ N
Where Cash Flow is the amount of money deposited each year, Interest Rate is the interest rate per year, and N is the number of years. In this case, Cash Flow is $190,000, Interest Rate is 9%, and N is 10 years.
Using the formula, we can calculate the present value:
Present Value = $190,000 / (1 + 0.09) ^ 10
Solving this equation, the present value of the saving cash flow is approximately $1,233,108.75 when the first deposit is made at the end of the year.
If the first deposit is made at the beginning of the year, we need to adjust the formula by adding an extra year of compounding:
Present Value = $190,000 / (1 + 0.09) ^ 10 * (1 + 0.09)
Solving this equation, the present value of the saving cash flow is approximately $1,347,732.42 when the first deposit is made at the beginning of the year.
Given that the total cost of building the resort after 10 years is $5,000,000, we can compare the present value of the saving cash flow with the total cost to determine if AAA has enough money. If the present value is greater than or equal to the total cost, then AAA has enough money to build the resort.
In this case, AAA does not have enough money to build the resort as the present value of the saving cash flow is lower than the total cost.