Final answer:
To calculate the monthly retirement withdrawals from a $400,000 account at 8% interest over 15 years, we use the annuity payment formula. One could withdraw approximately $3,956.74 per month for 15 years.
Step-by-step explanation:
Calculating Monthly Retirement Withdrawals
To determine how much one can withdraw each month from a retirement account that has $400,000 and earns 8% interest for 15 years, we can use a financial formula known as the annuity payment formula. The annuity payment formula considers the present value of the account, the interest rate, and the number of periods (months) to determine the fixed payment that can be withdrawn each period.
In this scenario, we need to make a series of monthly withdrawals that add up to $400,000 over the span of 15 years (which is 180 months) at an 8% annual interest rate, compounding monthly. The formula for the monthly withdrawal amount A is derived from the Present Value of Annuity formula:
P = (A / r) * [1 - (1 + r)^(-n)]
where:
- P is the present value of the annuity (the amount of money you have saved).
- A is the annuity payment per period.
- r is the interest rate per period.
- n is the total number of payments or periods.
To find A, rearrange the formula:
A = P * r / [1 - (1 + r)^(-n)]
In this case:
- P = $400,000
- Annual interest rate = 8%, so monthly rate r = 8% / 12 = 0.6667%
- r in decimal form = 0.006667
- n = 15 years * 12 months/year = 180 months
Substituting in the values, we calculate the monthly withdrawal amount.
A = $400,000 * 0.006667 / [1 - (1 + 0.006667)^(-180)] = $3,956.74 (approx)
Therefore, one could withdraw approximately $3,956.74 per month for 15 years from their retirement account under these circumstances.