To determine how much you will need to deposit each year until retirement, we can use the concept of future value of an ordinary annuity.
The formula to find the future value of an ordinary annuity is:
FV = P * [(1 + r)^n - 1] / r
Where:
FV = Future Value
P = Annual deposit amount
r = Interest rate per period
n = Number of periods
In this case, you want to withdraw $25,000 each year after retirement, and your account earns 4% interest. We need to find out how much you need to deposit each year until retirement (in 15 years) to achieve this goal.
Substituting the given values in the formula, we have:
FV = $25,000
r = 4% = 0.04 (expressed as a decimal)
n = 15 years
Now, we can rearrange the formula to solve for P (annual deposit amount):
P = FV * r / [(1 + r)^n - 1]
Plugging in the values:
P = $25,000 * 0.04 / [(1 + 0.04)^15 - 1]
Now, let's calculate it step by step:
Step 1: Calculate the numerator
Numerator = $25,000 * 0.04 = $1,000
Step 2: Calculate the denominator
Denominator = (1 + 0.04)^15 - 1
Denominator = (1.04)^15 - 1
Step 3: Calculate the denominator expression inside the parentheses (1.04)^15
Denominator = (1.04)^15 ≈ 1.7488
Step 4: Subtract 1 from the denominator expression
Denominator = 1.7488 - 1 ≈ 0.7488
Step 5: Calculate the final result
P = $1,000 / 0.7488
P ≈ $1,337.92
Therefore, you will need to deposit approximately $1,337.92 each year until retirement to achieve your retirement goal of being able to withdraw $25,000 annually.