Final answer:
Purchase a $50,000 sailboat in 5 years, considering a 4% inflation rate and a 7% annual return on investment, one must deposit $42,919.61 today.
Step-by-step explanation:
The student is asking how much money needs to be deposited today in an account that earns 7% per year to purchase a sailboat in 5 years that costs $50,000 today, taking into account an inflation rate of 4% per year. To answer this, we need to calculate the future cost of the sailboat accounting for inflation and then use the present value formula to determine how much to deposit today.
The future cost of the sailboat can be found using the formula for future value with inflation: Future Cost = Present Cost * (1 + Inflation Rate)^Number of Years. Therefore:
Future Cost = $50,000 * (1 + 0.04)^5 = $50,000 * (1.04)^5
Future Cost ≈ $60,941.12
Now we need to find the present value of $60,941.12 that needs to be deposited into an account with an annual return of 7%. The formula for the present value is: Present Value = Future Value / (1 + Rate of Return)^Number of Years, so:
Present Value = $60,941.12 / (1 + 0.07)^5
Present Value ≈ $42,919.61
Therefore, you would need to deposit $42,919.61 today to have enough money to purchase the sailboat in 5 years.