How Much Can You Withdraw Annually for 5 Years with a Birthday Deposit of $26,500?
What is the annual withdrawal amount for 5 years?
If the first withdrawal occurs at the beginning of the second year, how much can you withdraw annually for 5 years from an account that had $26,500 deposited on your 18th birthday with an interest rate of 11.25% compounded annually?
Annual Withdrawal Amount Calculation
To determine how much you can withdraw annually for 5 years, we use the formula for the future value of an ordinary annuity.
Firstly, calculate the future value (FV) of the deposit after 5 years:
Calculating Annual Withdrawal Amount
Using the formula for future value (FV) of an ordinary annuity:
FV = P(1 + r)^n
Given:
P = $26,500
r = 11.25%
n = 5 years
Calculate FV:
FV = $26,500(1 + 0.1125)^5
FV = $26,500(1.1125)^5
FV ≈ $26,500(1.7327)
FV ≈ $45,936.55
Now, determine the annual withdrawal amount using the formula for the present value of an ordinary annuity:
PV = A[(1 - (1 + r)^(-n))/r]
Substitute the values:
$45,936.55 = A[(1 - (1 + 0.1125)^(-5))/0.1125]
Solve for A:
A ≈ $45,936.55 / [(1 - 0.68301)/0.1125]
A ≈ $16,277.81
Therefore, you can withdraw approximately $16,277.81 annually for 5 years if the first withdrawal occurs at the beginning of the second year.