You are planning to save for retirement over the next 15 years. To do this, you will invest $1,100 a month in a stock account and $500 a month in a bond account. The return on the stock account is expected to be 7%, and the bond account will pay 4%. When you retire, you will combine your money into an account with a 5% return. How much can you withdraw each month during the retirement assuming a 20-year withdrawal period?
To answer this question, we need to calculate the future value of the monthly investments made in the stock and bond accounts over the next 15 years.
Let's start with the stock account:
Using the formula for future value of an ordinary annuity, we can calculate the future value of the stock account:
Future Value of Stock Account = Monthly Investment × [((1 + Annual Return)^(Number of Years) - 1) / Annual Return]
= $1,100 × [((1 + 0.07)^(15) - 1) / 0.07]
Calculating this expression, we find that the future value of the stock account will be $299,185.35.
Now, let's calculate the future value of the bond account:
Following the same formula, the future value of the bond account will be:
Future Value of Bond Account = Monthly Investment × [((1 + Annual Return)^(Number of Years) - 1) / Annual Return]
= $500 × [((1 + 0.04)^(15) - 1) / 0.04]
Calculating this expression, we find that the future value of the bond account will be $106,065.87.
Next, we combine the two future values:
Total Future Value = Future Value of Stock Account + Future Value of Bond Account
= $299,185.35 + $106,065.87
= $405,251.22
Now, using the future value and a 5% return, we can calculate the amount that can be withdrawn each month during the 20-year withdrawal period.
Using the formula for the future value of an ordinary annuity, but solving for the payment amount, we have:
Withdrawal Amount = Future Value × (Annual Return / ((1 + Annual Return)^(Number of Years) - 1))
= $405,251.22 × (0.05 / ((1 + 0.05)^(20) - 1))
Calculating this expression, we find that you can withdraw approximately $3,219.35 each month during the 20-year retirement period.
Therefore, you can withdraw approximately $3,219.35 each month during retirement assuming a 20-year withdrawal period.