Assume that your father is now $50$ years old, plans to retire in $10$ years, and expects to live for $25$ years after he retires $-$ that is$,$ until age $85.$ He wants his first retirement payment to have the same purchasing power at the time he retires as $$45,000$ has today. He wants all his subsequent retirement payments to be equal to his first retirement payment. $($Do not let the retirement payments grow with inflation: Your father realizes that if inflation occurs the real value of his retirement income will decline year by year after he retires$).$ His retirement income will begin the day he retires, $10$ years from today, and he will then receive $24$ additional annual payments. Inflation is expected to be $5\%$ per year from today forward. He currently has $$25,000$ saved and expects to earn a return on his savings of $8\%$ per year with annual compounding.Required Annuity Payments

Step $1.$ Calculate retirement payments, beginning at $t=10$

Fixed retirement payments

Step $2.$ Calculate the value of current savings at $t=10$

Value of current savings, $10$ years from today

Step $3.$ Calculate the value of the annuity due of retirement

payments at $t=10$

Value of annuity due

Step $4.$ Calculate the net amount that must be accumulated at $t=10$

to receive desired retirement payments

Net amount needed in $10$ years

Step $5.$ Calculate the value of annual deposit needed to meet desired

retirement goal

Value of annual deposit to meet retirement goal