you want to be able to withdraw 25,000 from your account each year after your retire. you expect to retire in 15 years.
If your account earns 4% interest, how much will you need to deposit each year until retirement to achieve your retirement goal?
To determine how much you need to deposit each year, we can use the future value of an ordinary annuity formula. The formula is:
FV = P * ((1 + r)^n - 1) / r
Where:
FV = Future value (the retirement goal of 25,000)
P = Deposit amount each year
r = Interest rate per period (4% or 0.04)
n = Number of periods (15 years)
Substituting the given values into the formula, we have:
25,000 = P * ((1 + 0.04)^15 - 1) / 0.04
Let's solve for P:
25,000 * 0.04 = P * ((1.04)^15 - 1)
1,000 = P * (1.749005819 - 1)
1,000 = P * 0.749005819
Dividing both sides by 0.749005819:
P = 1,336.1983
Therefore, you will need to deposit approximately $1,336.20 each year until retirement to achieve your retirement goal of withdrawing $25,000 per year.
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.
Major information is missing from this question.
1. Is this a perpetuity? That is, does the $25,000 come from a fund that keeps
earning 4% per year in interest?
2. Is this a life annuity? Then you will need mortality tables, which are not standard
( the probability of a 65 year old from Canada to live to 95 is not the same as
the prob of a 65 year old from Somalia)
3. No age is given for the start of the 15 year period of deposits.
etc