Sullivan says she will not retire unless she has 1.5 million dollars in her 401K. She is 23 now. How much money does she need to put into her IRA each month if she wants to retire early at age 60 assuming she can average a 8.1% return.
To calculate how much money Sullivan needs to put into her IRA each month, we can use the future value formula for regular contributions, also known as the annuity formula:
FV = P * [(1 + r)^n - 1] / r
Where:
FV is the future value of the investment,
P is the regular payment (monthly contribution),
r is the periodic interest rate (8.1% divided by 12 months),
n is the number of periods (number of months until retirement - (60 - 23) * 12).
To find the monthly contribution (P), we need to rearrange the formula:
P = FV * r / [(1 + r)^n - 1]
Now, let's plug in the values into the formula:
FV = $1,500,000 (Sullivan's desired retirement savings)
r = 8.1% / 12 = 0.675% (monthly interest rate)
n = (60 - 23) * 12 = 444 (number of months until retirement)
P = $1,500,000 * 0.675% / [(1 + 0.675%)^444 - 1]
Using a calculator or spreadsheet, evaluate the expression in square brackets and then calculate the result:
P ≈ $1,500,000 * 0.00675 / 5.057
P ≈ $20,062.04
Therefore, Sullivan needs to contribute approximately $20,062.04 into her IRA each month to reach her retirement goal of $1.5 million by age 60, assuming an average return of 8.1%.