Question

Jerry and Jenny are 25 years old and plan on retiring at age 67 and expect to live until age 100. Jenny currently earns $150,000 and they expect to need $150,000 per year in today’s dollars in retirement. Jerry is a stay at home dad. They also expect that Social Security will provide $40,000 of benefits in today’s dollars at age 67. Jenny has been saving $5,000 annually in her 401(k) plan. Their son, Jazz, was just born and is expected to go to college in 18 years. They want to save for Jazz’s college education, which they expect will cost $20,000 in today’s dollars per year and they are willing to fund 5 years of college. They were told that college costs are increasing at 7% per year, while general inflation is 3%. They currently have $100,000 saved in total and they are averaging a 10% rate of return and expect to continue to earn the same return over time. Based on this information, what should they do?

   

They are doing just fine and should continue doing what they are doing.

   

They should increase their annual savings by about 10 percent and they should be fine.

   

They have saved enough to fund retirement and Jazz’s education and can stop saving if they wish.

   

They need to increase their annual savings by about $5,000 now if they want to fund college in addition to retirement.

Write out your steps on how you obtained the answer

The questions I found already posted do not appear to have the correct answer and I am trying to learn this for my class

Answer 1

First we need to draw a timeline.

Current Age of the Couple - 25 Years

Retirement Age - 67 Year

Life Expectation - 100 Year

Time to Retirement = Retirement Age - Current Age = 67 - 25 = 42 years

Life Post Retirement - Life Expectation - Retirement Age = 100 - 67 = 33 years

Time for son to go for College - 18 years

Now we need to divide the goal of the couple into two parts

a. Amount Required Post Retirement

b. Amount Required to fund Son's College Education for Five Years

we will take each part separately and than solve for the answer

First Part Amount Required Post Retirement

Expenses in Today's Dollar Value Post Retirement - $150,000

Expenses that we will be funded by social security in today's dollar terms - $40,000

Expenses that will be funded by savings - 150000-40000 = $110,000

So we would be needing $110,000 per year in today's dollar term post-retirement.

So what is the amount of money we would be required in the first year of retirement?

Future Value = Present Vaue * (1+inflation rate)^time

Present Value is $ 110,000

Inflation Rate is 3%

Time (Time to retirement) is 42 years

Future Value = 110,000 * (1+.03)^42 = $380676.5

$380676.5 is the amount required in the first year of retirement, and this will grow by 3% every year for next 33 years post retirement.

Now an important part is how to factor inflation in the discount rate.

Our Discount Rate is 10% but the annuity will grow by 3% every year. So we need to factor inflation in the discount rate.

Real Discount Rate = (1+Nominal Discount Rate)/(1+Inflation)-1

Real Discount Rate = (1+10%)/(1+3%)-1 = 6.8%

PV at the Age of 67 of the amount needed post-retirement

Annuity = PMT = $380676.5

Years post Retirement = NPER = 33

Discount Rate = Rate = 6.8%

Excel Formula - PV(rate,nper,pmt)

PV = $4,959,632.5

This is the amount of money the couple should have at the time of retirement.

The Present Value (when couple are 25 years old) is

PV = FV/(1+Discount Rate)^time

FV is $4,959,632.5

Discount Rate is 10%

Time (time to retire) is 42 Years

PV = 4959632.5/(1+10%)^42 = $ 90,564.23

Present Value of the amount required for retirement is $90,564.23

Second Part Amount Required to fund Son's College Education for Five Years

Current Value of College Education per year - $20,000

Time for Son to go to college - 18 years

Increase in College fees per year - 7%

College Fees After 18 years = PV * (1+r)^t = 20000 * (1+7%)^18 = $67,597.65

The fees for the first year of college after 18 years is $67,597.65

Similarly the fees for 5 years of college and their PV

Year	Formula	Fees	Formula for PV	PV of the Fees
1		67598.65	67598.64/1	67598.65
2	67598.65*(1.07)^1	72330.56	72330.55/1.1	65755.05
3	67598.65*(1.07)^2	77393.69	77393.69/1.1^2	63961.73
4	67598.65*(1.07)^3	82811.25	82811.25/1.1^3	62217.32
5	67598.65*(1.07)^4	88608.04	88608.04/1.1^4	60520.48
				320053.23

Discounting is done using the rate of return i.e. 10%

Amount needed after 18 years for college education of the son is $ 320,053.23

Amount needed now for the education = FV/(1+r)^t = 320053.23/(1+10%)^18 = $57,564.39

Present Value of the amount required for son's education is $ 57,564.39

Total Amount Required right now for both the goals = PV of Retirement + PV of Son's Education = 90564.23 + 57564.39 = $ 148,128.62

Total Amount Needed Right now (at the age of 25) is $ 148,128.62

Savings

Currently, the couple has $100,000 in savings

They are saving $5,000 annually in 401K pension

PV of the Future Savings

Savings = PMT = $5,000

Time = NPER = 42 years

Rate of Return = Rate = 10%

PV(Rate,NPER,PMT) = PV = $49,087

Present Value of Future Savings is $49,087

Total Savings = Current Savings + PV of Future Savings = 100,000 + 49,087 = $149,087

Savings vs Expenses

Current Value of Savings = $149,087

Current Value of Expenses = $148,128.62

Savings is marginally greater than expenses, therefore they should continue with what they are doing