Question

John and Jane Smith are a middle class couple that spends $4,000.00 a month.  If John and Jane want to retire at the age of 67 (and they are now 27):

1. How much money will they be spending per month assuming 3% inflation?  How much is that per year?  Assume that social security is still in existence and will meet four tenths (or 40%) of their spending needs.
2. Assume that John and Jane primarily save for retirement through their 401(k) plans at work. Please also assume that they can get an ending after-tax return of 3.75% on their retirement nest egg.  You would get this rate if you assumed a 5% return on retirement assets that are invested in low-risk securities (5% x (1-.25 tax rate = .75) = 3.75%).  Hint: If you divide their annual retirement spending by 3.75% you will get the amount of the nest egg they need for retirement.
3. Also assume that during their working years from age 27 to 67 they earn a 7% return on their 401(k) investments.  How much money will they need to set aside in their 401(k) plans per month and per year in order to have an adequate retirement nest egg that compensates for the other 60% of their living expenses that social security does not cover.

PLEASE NOTE: Although their mortgage may go away and some other expenses may go away when they retire, it is safe to say that their out of pocket medical costs will greatly increase.  Thus, please make the assumption that the monthly and annual amounts of money they will spend in retirement years are equivalent to the amounts they are spending during their working years.

Answer 1

Note for references for Answers :

Monthly Spending  $4,000.00

Current Age = 27 Years

Retirement age 67 Years

Saving Period = 40 years( being 67yrs -27yrs)

Inflation rate = 3%

Return on investment = 7%

after-tax return on retirement nesting egg = 3.75%

Social Security contribution = 40% (pension)

Answer :

How much money will they be spending per month assuming 3% inflation?  How much is that per year?  Assume that social security is still in existence and will meet four tenths (or 40%) of their spending needs.

Ans :

Required monthly spends after retirement at 3% inflation

= $ 4000(1+0.03)^40= $ 13048

Yearly retirement spends = $ 13048*12= $ 156576

40% support by Social security Scheme= $ 5219/Month or $ 62630/Annum

Required 60% of Montly spending post retirement  =$ 7829/Month or $93946/Annum ( after 40 years)

Assume that John and Jane primarily save for retirement through their 401(k) plans at work. Please also assume that they can get an ending after-tax return of 3.75% on their retirement nest egg.  You would get this rate if you assumed a 5% return on retirement assets that are invested in low-risk securities (5% x (1-.25 tax rate = .75) = 3.75%).  Hint: If you divide their annual retirement spending by 3.75% you will get the amount of the nest egg they need for retirement.

Ans :

Nest egg they need for retirement at 3.75% = $93946/3.75%= $ 2,505,226

(Being Annual Retirement spends after Social Security pension of 40% of spends) applied at an interest rate of 3.75%

Also assume that during their working years from age 27 to 67 they earn a 7% return on their 401(k) investments.  How much money will they need to set aside in their 401(k) plans per month and per year in order to have an adequate retirement nest egg that compensates for the other 60% of their living expenses that social security does not cover

Ans :

Monthly savings required in 401(k) investment scheme to create a nesting egg value of $ 2505226 after 40 Years @ 7% ROI on the scheme

Formulae for annuity certain is as follows, assuming the monthly savings are deposited in the scheme at the end of every month for next 40 Years.

Rate of Interest per month = 7%/12= 0.58%

No of Months(Instalments) in 40 Years= 40*12= 480

Formula for Finding the Periodic payment(R), Given A: R = A/(1+〖(1-(1+((j/m) )〗^(-(n-1))/(j/m))

Where A= Amount i.e $ 2505226

J = Interest rate= 0.58% i.e 0.0058

N= No of months= i.e 480

R = =2505266/((((1+((0.0058)/1))^(480+1)-1)/((0.0058)/1)-1))

= $ 959.66