You have \( \$ 500,000 \) 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 25 years?

We start with the formula for the monthly withdrawal \( M \) from a principal \( P \) that earns a monthly interest rate \( r \) over \( n \) months: \[ M = P \times \frac{r(1+r)^n}{(1+r)^n - 1} \] **Step 1. Identify the given values.** - Principal: \( P = 500,\!000 \) - Annual interest rate: \( 8\% \) - Monthly interest rate: \[ r = \frac{0.08}{12} \approx 0.0066667 \] - Duration: 25 years - Total number of months: \[ n = 25 \times 12 = 300 \] **Step 2. Substitute the values into the formula.** \[ M = 500,\!000 \times \frac{0.0066667 \times (1+0.0066667)^{300}}{(1+0.0066667)^{300} - 1} \] **Step 3. Compute \((1+r)^n\).** \[ (1+0.0066667)^{300} \approx 7.34 \] **Step 4. Compute the numerator and denominator.** - Numerator: \[ r(1+r)^n \approx 0.0066667 \times 7.34 \approx 0.04893 \] - Denominator: \[ (1+r)^n - 1 \approx 7.34 - 1 = 6.34 \] **Step 5. Calculate the fraction and then the monthly withdrawal \( M \).** \[ \text{Fraction} \approx \frac{0.04893}{6.34} \approx 0.007714 \] \[ M \approx 500,\!000 \times 0.007714 \approx 3,\!857 \] Thus, you will be able to pull out approximately \( \$3,\!857 \) each month.