You have $400,000 saved for retirement. Your account earns 8% interest. How much will you be able to pull out each month, if you want to be able to take withdrawals for 15 years?
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To determine how much you will be able to withdraw each month, we can use the concept of annuities. Annuities are a series of equal periodic payments made over a specified period of time.
First, we need to calculate the future value of your retirement savings, taking into account the interest rate and the duration of withdrawals. The future value formula for an ordinary annuity is:
FV = P * [(1 + r)^n - 1] / r
Where:
FV = Future Value
P = Payment amount
r = Interest rate per period
n = Number of periods
In this case, you want to withdraw money for 15 years, and the interest rate is 8% per year. Since you want to withdraw a fixed amount each month, the number of periods (n) will be 15 years multiplied by 12 months per year (n = 180).
Using this information, we can rearrange the formula to solve for the payment amount (P):
P = FV * (r / [(1 + r)^n - 1])
Now, let's plug in the values and calculate the monthly withdrawal:
FV = $400,000
r = 0.08/12 (monthly interest rate)
n = 180
P = $400,000 * (0.08/12) / [(1 + 0.08/12)^180 - 1]
Calculating this equation will give you the monthly withdrawal amount you can take from your retirement savings for 15 years.