You want to be able to withdraw $45,000 from your account each year for 30 years after you retire.
You expect to retire in 15 years.
If your account earns 5% interest, how much will you need to deposit each year until retirement to achieve your retirement goals?
To calculate the amount you need to deposit each year until retirement, we can use the concept of future value of annuity. The future value of an annuity is the total value of a series of equal payments compounded over a specified period of time.
In this case, you want to withdraw $45,000 from your account each year for 30 years after you retire. To determine the amount you need to deposit each year until retirement, we first calculate the future value of this annuity.
Step 1: Calculate the future value of the annuity.
The future value of an annuity can be calculated using the formula:
FV = PMT × [(1 + r)^n - 1] / r
Where:
FV = Future Value of the annuity (total value you want to retire with)
PMT = Amount you want to withdraw each year ($45,000)
r = Interest rate per compounding period (5% or 0.05)
n = Number of compounding periods (30 years)
Using these values, we can calculate the future value:
FV = $45,000 × [(1 + 0.05)^30 - 1] / 0.05
Step 2: Solve for the amount to be deposited each year until retirement.
The amount to be deposited each year until retirement could be referred to as the annuity payment or the present value of the annuity. Rearranging the formula for future value of annuity, we can solve for the annuity payment:
PMT = FV × (r / [(1 + r)^n - 1])
Substituting the values we have:
PMT = [$45,000 × [(1 + 0.05)^30 - 1] / 0.05] × (0.05 / [(1 + 0.05)^15 - 1])
Simplifying this calculation will give you the amount you need to deposit each year until retirement.