How much money will I need to have at retirement so I can withdraw $60,000 a year
for 20 years from an account earning 8% compounded annually?
a. How much do you need in your account at the beginning
b. How much total money will you pull out of the account?
c. How much of that money is interest?
a. You will need $1,072,945.20 in your account at the beginning.
b. You will pull out a total of $1,200,000 from the account.
c. The interest earned will be $127,054.80.
To calculate the amount of money you will need at retirement, you can use the formula for the future value of an annuity. The formula is:
FV = P * [(1 + r)^n - 1] / r
Where:
FV = Future value (amount of money needed at retirement)
P = Payment per period ($60,000 per year)
r = Interest rate per period (8% compounded annually)
n = Number of periods (20 years)
a. To find out how much you need in your account at the beginning, you can rearrange the formula:
FV = P * [(1 + r)^n - 1] / r
FV * r = P * [(1 + r)^n - 1]
FV * r / [(1 + r)^n - 1] = P
Plugging in the values:
FV = ?
P = $60,000
r = 0.08 (8%)
n = 20 years
FV * 0.08 / [(1 + 0.08)^20 - 1] = $60,000
Solving for FV:
FV * 0.08 / 1.08^20 - 1 = $60,000
FV * 0.08 / 3.172 = $60,000
FV * 0.02516835 = $60,000
FV = $60,000 / 0.02516835
FV ≈ $2,381,046.80
So, you will need approximately $2,381,046.80 in your account at the beginning.
b. To calculate the total amount of money you will pull out of the account, you can multiply the annual withdrawal amount by the number of years:
Total = Annual Withdrawal * Number of Years
Total = $60,000 * 20
Total = $1,200,000
Therefore, you will pull out a total of $1,200,000 from the account.
c. To find out how much of that money is interest, you can subtract the initial amount you had in the account from the total amount you pulled out:
Interest = Total - Initial Amount
Interest = $1,200,000 - $2,381,046.80
Interest ≈ -$1,181,046.80
The negative result means that the $1,181,046.80 represents the initial amount you had in the account, and the remaining $1,200,000 is the interest earned.
To calculate the amount of money you need to have at the beginning of your retirement to withdraw $60,000 per year for 20 years, let's use the concept of future value of an annuity.
a. To find out how much you need to have in your account at the beginning, we'll use the future value of an annuity formula:
FV = PMT * [(1 + r)^n - 1] / r
Where:
FV is the future value of the annuity
PMT is the annual withdrawal amount ($60,000)
r is the interest rate per period (8% or 0.08)
n is the number of periods (20 years)
Plugging the values into the formula:
FV = $60,000 * [(1 + 0.08)^20 - 1] / 0.08
Using a calculator, the result is approximately $962,174.16.
Therefore, you would need approximately $962,174.16 in your retirement account at the beginning to be able to withdraw $60,000 per year for 20 years.
b. To calculate the total amount of money you will pull out of the account, you need to multiply the annual withdrawal amount by the number of years:
Total withdrawal = Annual withdrawal amount * Number of years
Total withdrawal = $60,000 * 20
The total withdrawal would be $1,200,000.
Therefore, you will pull out a total of $1,200,000 from the account over 20 years.
c. To find out how much of that money is interest, subtract the initial amount you had in the account from the total withdrawal amount:
Interest earned = Total withdrawal - Initial amount
Interest earned = $1,200,000 - $962,174.16
The interest earned would be approximately $237,825.84.
Therefore, approximately $237,825.84 of the total withdrawal amount would be interest earned.