Question

You are just 23 years old and you have $10,000 in your retirement saving accounts. You expect to retire at the age of 70 (work for 47 more years) and expect to live for another 30 years after your retirement. On the day you retire, you want to have enough money in our retirement saving accounts such that you are able to draw $10,000 per month for 30 years. You are conservative in your estimate of interest rate and expect to earn on an average 4.25% on your money during the entire period.

(a) How much you need to deposit each month throughout your working years to achieve your post retirement income goal, if you plan to die on the day you spend your last penny?

(b) There is one more complication that you realized only at the last day of your age 35! And the end of your age 55 (in 20 year time), you expect your only kid to join a top notch MBA program. You want to help your kid achieve his/her career goal and you plan to give him/her a onetime grant of $150,000 when he joins the program. How much you need to additionally save each month from age 35 onwards to achieve enough funds at the end of age 70 to meet your original retirement income goal as well as your child’s educational goal?

(c) Suppose your financial situations at age 35 is such that you cannot increase your monthly savings in the pension account. If you still want to give your kid a onetime grant of $150,000 at the end of your age 55, how much reduction in your post retirement monthly income you have to absorb in order to accommodate the additional expenditure of $150,000.

Answer 1

Part (a)

Retirement kitty size required at the time of retirement = enough money in our retirement saving accounts such that you are able to draw $10,000 per month for 30 years = PV of annuity 10,000

A = 10,000; r = 4.25% / 12 = 0.003542; n = 12 x 30 = 360

Retirement kitty size = A / r x [1 - (1 + r)^-n] = 10,000 / 0.003542 x [1 - (1 + 0.003542)^-360] =  2,032,769

This is the FV, we need PMT,

Monthly deposit = -PMT (Rate, Nper, PV, FV) = - PMT (0.003542, 47 x 12, -10000, 2032768) = 1,093.72 = 1,094 (Please round it off as per your requirement)

Part (b)

Incremental monthly deposit = - PMT (Rate, Nper, PV, FV) = - PMT (0.003542, 20 x 12, 0, 150000) = $ 397.60 = $ 398 (Please round it off as per your requirement)

Part (c)

Reduction in kitty size due to unexpected withdrawal of 150,000 at the end of year 55 = 150,000 x (1 + r)^{n - t} = 150,000 x (1 + 0.003542)^{70 - 55} = $158,169

Hence, new kitty size = 2,032,769 - 158,169 = $  1,874,599

Hence, new post retirement monthly income = PMT (Rate, Nper, PV, FV) = PMT (0.003542, 12 x 30, -1874599, 0) = $ $9,221.90

Hence, reduction in monthly income = 10,000 - $9,221.90 = $ $778.10 (Please do round it off as per your requirement)