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?
A. $2,636.19
B. $2,904.11
C. $3,008.21
D. $3,037.36
E. $3,406.97
When I'm trying to solve, I end up with $3,113.04 and cannot figure out where I'm wrong. Can anyone help?
You are using the percentages as APR. They are in EAR currently, convert them and you should get the right answer.
To calculate the amount you can withdraw each month during retirement, you need to determine the future value of your retirement savings. In this scenario, you are investing $1,100 a month in a stock account, which has an expected return of 7%, and $500 a month in a bond account, which has a return of 4%.
First, let's calculate the future value of your stock account after 15 years. Using the formula for the future value of an ordinary annuity:
Future Value (Stock Account) = P * [((1 + r)^n - 1) / r]
Where:
P = Monthly investment amount ($1,100)
r = Monthly interest rate (7% / 12)
n = Number of months (15 * 12)
Plugging in the values:
Future Value (Stock Account) = $1,100 * [((1 + 0.07/12)^(15*12) - 1) / (0.07/12)]
Next, let's calculate the future value of your bond account after 15 years:
Future Value (Bond Account) = P * [((1 + r)^n - 1) / r]
Where:
P = Monthly investment amount ($500)
r = Monthly interest rate (4% / 12)
n = Number of months (15 * 12)
Plugging in the values:
Future Value (Bond Account) = $500 * [((1 + 0.04/12)^(15*12) - 1) / (0.04/12)]
Now, let's combine the future values of both accounts into a single account with a 5% return. To do this, you can simply add the future values of the stock and bond accounts:
Total Future Value = Future Value (Stock Account) + Future Value (Bond Account)
Finally, we need to calculate the monthly withdrawal amount during retirement for a period of 20 years. Using the formula for the present value of an ordinary annuity:
Withdrawal Amount = Total Future Value * (r / ((1 + r)^n - 1))
Where:
Total Future Value = Future value of combined accounts
r = Monthly interest rate during retirement (5% / 12)
n = Number of months during retirement (20 * 12)
Plugging in the values:
Withdrawal Amount = Total Future Value * (0.05/12) / ((1 + 0.05/12)^(20*12) - 1)
Once you calculate this expression, you should arrive at the correct answer. If you are getting a different result, please ensure that you are correctly applying the formulas and performing the calculations accurately.