Final answer:
To calculate the necessary retirement savings for withdrawing $8,600 per month over 25 years with a 6% annual return, use the Present Value of an Annuity formula. This calculation will give you the total amount needed by your 63rd birthday to support your planned retirement withdrawals.
Step-by-step explanation:
To calculate the amount of money needed to withdraw during retirement, we need to determine the total amount to be withdrawn and then find the present value of that amount. If you plan to withdraw $8,600 per month for 25 years after retiring at 63, you're looking at 25 years x 12 months = 300 monthly withdrawals. Given an annual interest rate of 6%, we can use a financial formula known as the Present Value of an Annuity formula.
The Present Value of an Annuity formula is as follows:
PV = PMT × {(1 - (1 + r)^(-n)) / r}
Where:
- PV = Present Value
- PMT = Monthly payment (withdrawal amount)
- r = Monthly interest rate (annual rate / 12)
- n = Total number of payments
Annual interest rate is 6%, so the monthly rate (r) is 0.06/12. The number of payments (n) is 300. Plugging in the values:
PV = $8,600 × {(1 - (1 + (0.06/12))^(-300)) / (0.06/12)}
When you do the math, you get the present value (PV), which is the total amount you need to have saved by your 63rd birthday to fund your retirement withdrawals.