Question

You plan to retire 37 years from now. You expect that you will live 25 years after retiring. You want to have enough money upon reaching retirement age to withdraw $110,000 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 (62 years from now). You plan to accumulate the retirement fund by making equal annual deposits at the end of each year for the next 37 years. You expect that you will be able to earn 10% per year on your deposits. However, you only expect to earn 8% per year on your investment after you retire since you will choose to place the money in less risky investments. What equal annual deposits must you make each year to reach your retirement goal?

Answer 1

Withdrawals: $ 110000 per annum at the beginning of each year for 25 years, Final Value Leftover = $ 2500000

Interest Earned = 8 %

Therefore, Present value of withdrawals and leftover at the end of Year 37 = PV(37) = 110000 x (1/0.08) x [1-{1/(1.08)^(25)}] x (1.08) x [2500000 / (1.08)^(25)] = $ 1633208.17

Deposits: Let the equal annual end of Year deposits be $ K, tenure of deposits = 37 years and Interest Earned = 10 %

Therefore, Future Value of Deposits at the end of year 37 = FV(37) = K x (1.1)^(36) + ..............+ K x (1.1) + K = K x [{(1.1)^(37)-1}/{1.1-1}] = K x 330.039

Now, as per the laws of time-value of money, FV(37) = PV(37)

K x 330.039 = 1633208.17

K = 1633208.17 / 330.039 = $ 4948.52