Final answer:
The annual payout from an annuity of $685,000 over 22 years at an interest rate of 4.15% is approximately $46,482.64. The exact amount may vary slightly based on the compounding frequency and rounding methods used.
Step-by-step explanation:
To calculate the annual payout from an annuity of $685,000 over 22 years at an interest rate of 4.15%, we use the annuity payout formula:
- P = principal amount (initial investment)
- r = annual interest rate (decimal)
- n = number of payments per year
- t = number of years
The formula is:
A = P * [r(1 + r)^nt] / [(1 + r)^nt - 1]
Plugging in the values:
A = 685,000 * [0.0415(1 + 0.0415)^(22)] / [(1 + 0.0415)^(22) - 1]
Solving for A (the annual payout), we get:
A = 685,000 * [0.0415(1 + 0.0415)^22] / [(1 + 0.0415)^22 - 1] = $46,482.64
This is an approximate value, and the actual calculations could slightly vary depending on the method used for rounding and the compounding frequency of the annuity.