Your father is 50 years old and will retire in 10 years. He expects to live for 25 years after he retires, until he is 85. He wants a fixed retirement income that has the same purchasing power at the time he retires as $40,000 has today. (The real value of his retirement income will decline annually after he retires.) His retirement income will begin the day he retires, 10 years from today, at which time he will receive 24 additional annual payments. Annual inflation is expected to be 3%. He currently has $50,000 saved, and he expects to earn 7% annually on his savings.

Retirement income today: $40,000
Years to retirement: 10
Years of retirement: 25
Inflation rate: 3.00%
Savings: $50,000
Rate of return: 7.00%

How much must he save during each of the next 10 years (end-of-year deposits) to meet his retirement goal? Do not round your intermediate calculations. Round your answer to the nearest cent.

To calculate the end-of-year deposits the father needs to make to meet his retirement goal, we can use the future value of an ordinary annuity formula. This formula helps us find the future value of a series of equal payments made at regular intervals.

First, we need to find the future value of $40,000 at the time of the father's retirement, which is 10 years from now. We can use the formula [tex]FV = Pmt * [(1 + r)^n - 1] / r[/tex], where FV is the future value, Pmt is the annual deposit, r is the interest rate, and n is the number of periods.

Plugging in the given values, we can calculate the future value:

FV = $40,000 * [(1 + 0.03)^10 - 1] / 0.03

Simplifying the equation:

FV = $40,000 * (1.343916379) / 0.03

Calculating the result:

FV ≈ $45,855.86

Therefore, the father needs to save approximately $45,855.86 annually for the next 10 years to meet his retirement goal.