You plan to retire 33 years from now. You expect that you will live 27 years after retiring.
You want to have enough money upon reaching retirement age to withdraw $180,000 from
the account at the beginning of each year you expect to live, and yet still have $2,500,000 left
in the account at the time of your expected death (60 years from now). You plan to
accumulate the retirement fund by making equal annual deposits at the end of each year for
the next 33 years. You expect that you will be able to earn 12% per year on your deposits.
However, you only expect to earn 6% per year on your investment after you retire since you
will choose to place the money in less risky investments.
Required:
Calculate the equal annual deposits you must make each year to reach your retirement
goal.

1. Determine the total amount of money you will need at retirement. You want to be able to withdraw $180,000 at the beginning of each year for 27 years and still have $2,500,000 left at the end of 60 years. So, the total amount needed at retirement can be calculated as:

$180,000 x 27 years = $4,860,000

($2,500,000 + $4,860,000) = $7,360,000

2. Calculate the future value of your annual deposits. Since you plan to accumulate the retirement fund by making equal yearly deposits for the next 33 years, you can use the future value of an ordinary annuity formula:

FV = PMT x [(1 + r)^n - 1] / r

FV is the future value, PMT is the annual deposit, r is the interest rate, and n is the number of years.

3. Plug the values into the formula. In this case, the future value (FV) is $7,360,000, the interest rate (r) is 12% before retirement and 6% after retirement, and the number of years (n) is 33. We need to solve for the annual deposit (PMT).

4. First, calculate the future value of the annual deposits during the 33-year accumulation period (using a 12% interest rate):

$7,360,000 = PMT x [(1 + 0.12)^33 - 1] / 0.12

5. Solve for PMT using algebraic calculations:

PMT = $7,360,000 x (0.12 / [(1 + 0.12)^33 - 1])

PMT ≈ $4,334.94

Therefore, you must make equal annual deposits of approximately $4,334.94 for the next 33 years to reach your retirement goal of having enough money to withdraw $180,000 at the beginning of each year for 27 years and still have $2,500,000 remaining at the end.