Question

Grady​ Zebrowski, age​ 25, just graduated from​ college, accepted his first job with a ​$45 comma 000 ​salary, and is already looking forward to retirement in 40 years. He assumes a 3.5 percent inflation rate and plans to live in retirement for 20 years. He does not want to plan on any Social Security benefits. Assume Grady can earn a 6 percent rate of return on his investments prior to retirement and a 6 percent rate of return on his investments​ post-retirement to answer the following questions using your financial calculator. a.  Grady wants to replace 90 percent of his current net income. What is his annual need in​ today's dollars? b.  Using the table LOADING...​, Grady thinks he might have an average tax rate of 13 percent at retirement if he is married. Adjusting for​ taxes, how much does Grady really need per​ year, in​ today's dollars? c.  Adjusting for​ inflation, how much does Grady need per year in future dollars when he begins retirement in 40 ​years? d.  If he needs this amount for 20 ​years, how much does he need in total for​ retirement?​ (Hint: Use the​ inflation- adjusted rate of​ return.) e.  How much does Grady need to save per month to reach his retirement goal assuming he does not receive any employer match on his retirement​ savings? Click on the table icon to view the FVIF table LOADING.... Click on the table icon to view the PVIFA table LOADING.... Click on the table icon to view the FVIFA table LOADING.... a. ​Grady's annual need in​ today's dollars is ​$ nothing. ​(Round to the nearest​ dollar.)

Answer 1

Part (a):

Given, present salary= $45,000, Income replacement ratio= 90%

Therefore, amount needed on retirement in today’s Dollar = $45,000*90% = $40,500

Part (b):

Given, tax rate (T)= 13%

Therefore, amount needed on retirement in today’s Dollar, adjusted for tax= $40,500/(1-13%)

= $46,551.72

Part (c):

Inflation rate= 3.5%

Therefore, amount needed on retirement in today’s Dollar at the age of 40 (ie., in 15 years)= $46,551.72*FVIF(3.5%,15)= $46,551.72*1.6753488 =$77,990.37

Part (d):

Life in retirement expected=20 years

Rate of return on investment after retirement=6%

Inflation adjusted rate of return= 6%-3.5%= 2.5%

Therefore, amount needed at the time of retirement= $77,990.37*PVIFA(2.5%,20)

=$77,990.37*15.589162= $1,215,804.53

Part (e):

Rate of return on investment till retirement=6%

Amount to be saved every month during 15 years till retirement

= $1,215,804.53*SFF(6%,15 Years Monthly)= $1,215,804.53* 0.003439= $4,181