You contribute $1,000 annually to a retirement account for 8 years and stop making payments at the age of 25. Your twin brother (or sister whichever applies) opens and account at age 25 and contributes $1000 a year until retirement at 65 (40 years). You both earn 10% on your investments. How much can each of you withdraw for 20 years (that is, ages 66 through 85) from the retirement accounts?

Question

You contribute $1,000 annually to a retirement account for 8 years and stop making payments at the age of 25. Your twin brother (or sister whichever applies) opens and account at age 25 and contributes $1000 a year until retirement at 65 (40 years). You both earn 10% on your investments. How much can each of you withdraw for 20 years (that is, ages 66 through 85) from the retirement accounts?

Answer 1

To solve this problem, we need to calculate the future value of the retirement accounts for both you and your twin brother/sister.

First, let's calculate the future value of your retirement account. You contribute $1,000 annually for 8 years and earn a 10% return on your investment. We can use the formula for the future value of an ordinary annuity:

FV = P * [(1 + r)^n - 1] / r

Where:
FV = future value
P = payment per period ($1,000)
r = interest rate per period (10% or 0.10)
n = number of periods (8 years)

Plugging in the values:

FV = $1,000 * [(1 + 0.10)^8 - 1] / 0.10

Calculating this, we find that the future value of your retirement account is approximately $14,486.85.

Now, let's calculate the future value of your twin brother/sister's retirement account. They contribute $1,000 annually for 40 years and earn a 10% return on their investment. Using the same formula as before:

FV = $1,000 * [(1 + 0.10)^40 - 1] / 0.10

Calculating this, we find that the future value of your twin's retirement account is approximately $452,592.96.

Finally, to determine how much each of you can withdraw for 20 years (ages 66-85), we need to calculate the annual withdrawals from the retirement accounts. We will assume an annual withdrawal rate of 4% for both accounts.

For your retirement account, the annual withdrawals would be calculated as follows:

Annual Withdrawals = FV * withdrawal rate

Annual Withdrawals = $14,486.85 * 0.04

Calculating this, we find that you can withdraw approximately $579.46 annually for 20 years.

For your twin brother/sister's retirement account, the annual withdrawals would be:

Annual Withdrawals = $452,592.96 * 0.04

Calculating this, we find that your twin can withdraw approximately $18,103.72 annually for 20 years.

So, you can withdraw approximately $579.46 annually, while your twin brother/sister can withdraw approximately $18,103.72 annually during the ages of 66 through 85.