Question

Suppose you have just graduated Hofstra and accepted a job with a $100,000 salary. Your 401(K) will be maxed at 5% employee contribution and 1-1 employer match. You will work for exactly the next 45 years (for simplicity assume your salary is unchanged). At your 5 year review you will receive a one time $20,000 bonus which you will deposit in your retirement plan. You will live exactly 25 years after you retire. You plan to leave $200,000 to Hofstra to name a building after yourself. If you expect to earn 6% return annually, what are your annual withdrawals?

Answer 1

PMT = 5% + 5% = 10% x 100,000 = $ 10,000

FV = Future value = the accumulated amount at retirement = A / r x [(1 + r)ⁿ - 1] + Bonus x (1 + r)^{n - 5} = 10,000 / 6% x [(1 + 6%)⁴⁵ - 1] + 20,000 x (1 + 6%)^{45 - 5} =  2,333,149

This should be the PV of all the withdrawls and the amount you will to leave for Hofstra

If W is the annual withdrawls then,

PV of W as annuity + PV of 200,000 = 2,333,149

Or, W / r x [1 - (1 + r)^-n1] + 200,000 x (1 + r)^-n1 = 2,333,149

Or, W / 6% x [1 - (1 + 6%)^-25] + 200,000 x (1 + 6%)^-25 = 2,333,149

Hence, 12.78W + 46,600 = 2,333,149

Hence, W = (2,333,149 - 46,600) / 12.78 = $ 178,869 = annual withdrawls