Question

Jack and Jill are 41 years old and plan on retiring at age 65 and expect to live until age 95. Theycurrently earn $200,000 and expect to need $100,000 in retirement. They also expect that SocialSecurity will provide $24,000 of benefits in today’s dollars at age 65. They are saving $20,000 each intheir 401(k) plans and IRAs. Their son, Parker, is expected to go to college in 10 years. They want tosave for Parker’s college education, which they expect will cost $25,000 in today’s dollars and they arewilling to fund 4 years of college. They were told that college costs are increasing at 6% per year, whilegeneral inflation is 3%. They currently have $500,000 saved in total and they are averaging an 8% rateof return and expect to continue to earn the same return over time. Based on this information, whatshould they do?

Answer 1

Basesd on the information provided above, let us try to determine whether have they saved enough for their retirement and parker's education or not, and do they need to still invest or can stop further investments.

DAta Provided:

Earnings Rate : 8%

Current Age: 41 yrs

Retirement age: 65 yrs

Inflation rate: 3%

Life Expentancy: 95 yrs

Let us first determine the total amount which is to be funded:

They are expected to get retired at the age of 65

They need $100,000

Less: Social security which is to be provided at the age of 65 is $24,000

So total funds needed is $76,000

They are now 41 yrs of age, expected to retire at 65 yrs

Total number of years lefft to retire = 65 - 41 = 24 yrs

So the Future Value of $76,000 after 24 yrs at the age of retirement would be = 76,000 * (1+0.03)²⁴ = $154,492.35

The present Value of the Retirement Annuity can be calculated with the following formula:(at the age of 65)

PV = PMT ((1-(1/(1+r)ⁿ))/r)

n heree would be the difference beetween the life expentancy and retirement age = 95 - 65 = 30 yrs

PV of Retirement Annuity = $154,492.35((1-(1/1.048544)³⁰))/0.048544 = $2,532,092.39

Let us find the present value of the lumpsum of retirement annuity in todays value by discounting it with 8% interest for 24 years.

PV = $2,532,092.39/(1+0.08)²⁴ = $399,309.29

Now Let us find the Total o[f education Costs in today's Value:

Let us try to get the total of education cost in 10 yrs

Todays cost is $25,000

n = 10 yrs

interest rate = 6%

Value at the end of 10 years = 25000 * (1.06)¹⁰ = $44,771.19

$44,771.19 would be the fees for four years.

Total of education cost at the beginning of the year = PMT*((1-(1/(1+r)ⁿ))/r)

n = 4

r = 1.89

PMT = $44,771.19

PV = $44,771.19 ((1-1/(1+0.0189)⁴))/0.0189) = $174,171.32

Let us try to discount it to present value of todays time(that is disounting it for 10 years at current market interst rate)

PV = $174,171.32/(1.08)¹⁰  = $80,675.02

Now let us make the judgement:

PV of retirment = $2,532,092.39

PV of Education = $80,675.02

Total = $479,984.31

Less Investment Assets = $500,000

They still have surplus of $20,015.69

Therefore they need not specifically save for the meeting the future requirements. They already have saved enough of savings for their retirement and Parker's Education Cost. They can stop saving if they wish.