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?
To calculate how much each person can withdraw from their retirement accounts, we need to determine the future value of their investments after the contribution period. The future value (FV) can be calculated using the formula:
FV = P × (1 + r)^n
Where:
P = Annual contribution
r = Annual interest rate
n = Number of years
Let's calculate the future value for each person:
1. For the first person (who contributed for 8 years):
P = $1,000 (annual contribution)
r = 10% (annual interest rate)
n = 8 (number of years)
FV1 = $1,000 × (1 + 0.1)^8
FV1 = $1,000 × (1.1)^8
FV1 ≈ $1,000 × 2.1589
FV1 ≈ $2,158.90
2. For the second person (who contributed for 40 years):
P = $1,000 (annual contribution)
r = 10% (annual interest rate)
n = 40 (number of years)
FV2 = $1,000 × (1 + 0.1)^40
FV2 = $1,000 × (1.1)^40
FV2 ≈ $1,000 × 45.259
FV2 ≈ $45,259.00
Now that we have the future values for both individuals, let's calculate how much they can withdraw for 20 years (from ages 66 to 85).
1. For the first person (who contributed for 8 years):
Since this person stopped contributing but earned interest for 40 years (from age 25 to 65), the future value of their investment is $2,158.90.
Using this future value, we can calculate the annual withdrawal amount. Assuming they withdraw a fixed amount each year, we divide the future value by the number of years they want to withdraw:
Withdrawal1 = FV1 / 20
Withdrawal1 ≈ $2,158.90 / 20
Withdrawal1 ≈ $107.95 (approximately)
Therefore, the first person can withdraw approximately $107.95 per year for 20 years.
2. For the second person (who contributed for 40 years):
The future value for this person is $45,259.00.
Similarly, we calculate the annual withdrawal amount by dividing the future value by the number of years they want to withdraw:
Withdrawal2 = FV2 / 20
Withdrawal2 ≈ $45,259.00 / 20
Withdrawal2 ≈ $2,262.95 (approximately)
Therefore, the second person can withdraw approximately $2,262.95 per year for 20 years.
In summary, the first person can withdraw approximately $107.95 per year, while the second person can withdraw approximately $2,262.95 per year, both for 20 years (ages 66 to 85).