Final answer:
To determine the amount Dave needs to invest each month to retire with $2,000,000 in 37 years at an 11% investment return, we use the future value of an annuity formula, accounting for the monthly interest rate and the number of periods. Using a financial calculator or software is recommended to get the exact amount.
Step-by-step explanation:
Dave wants to have $2,000,000 on the day he retires (37 years from now). He is planning on earning 11.0% from his investments. To calculate how much Dave needs to invest per month to reach his goal, we can use the future value of an annuity formula:
Future Value of Annuity = Pmt [((1 + r)^nt - 1) / r]
Where:
- Pmt is the monthly payment amount,
- r is the monthly interest rate (annual rate divided by 12 months),
- n is the number of times the interest is compounded per year,
- t is the number of years.
We're looking for Pmt and we know the future value is $2,000,000, r is 11% per year (or about 0.009167 per month), n is 12 (since interest is compounded monthly), and t is 37 years.Plugging in the known values and solving for Pmt gives us the monthly investment amount that Dave needs to contribute to reach his retirement goal.It's important to use a financial calculator or an appropriate software tool to handle the calculations because they involve complex exponential equations that are not easily solvable without such tools. Once calculated, Dave will know the exact monthly amount required to achieve his retirement fund of $2,000,000.