Question

Fred and Louise are 38 years old and plan on retiring at age 67 and expect to live until age 95.
Fred currently earns $150,000 and they expect to need $100,000 in retirement. Louise is a stay at home
mom. They also expect that Social Security will provide $30,000 of benefits in today’s dollars at age
67. He has been saving $17,000 annually in his 401(k) plan. Their daughter, Ann, who was just
born, is expected to go to college in 18 years. They want to save for Ann’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 $400,000 saved in total and they are averaging a 7% rate of return and
expect to continue to earn the same return over time. Based on this information, what should they
do? Show work.

a. They have saved enough to fund retirement and Ann’s education and can stop saving if
they
wish.
b. They should continue to save what they are saving.
c. They need to increase their annual savings by about $5,000 now if they want to fund
college
in addition to retirement.
d. They need to increase their annual savings by about 10 percent and they should be
fine.

Answer 1

The correct answer is the first option, i.e. a. They have saved enough to fund retirement and Ann’s education and can stop saving if they wish.

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What they have:

They currently have $400,000 saved in total and they are averaging a 7% rate of return and expect to continue to earn the same return over time.

What they need:

Ann’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. The college costs are increasing at 7% per year.

The rate of increase in the fees is same as rate of return on the current saving. Hence both of them will grow at the same rate in future. Since, $ 400,000 (current saving) is good enough to take care of five years of college fees of 20,000 x 5 = 100,000 in today's term and since the two are growing at the same rate in future, current saving will take care of college education fees.

The social security benefits that they would receive on retirement is sufficient enough to fund their lifestyle post retirement.

• Social Security will provide $30,000 of benefits in today’s dollars at age 67. So, the benefits from social security at the time of retirement = 30,000 x (1 + inflation)^{(retirement age - current age)}= 30,000 x (1 + 3%)^{(67 - 38)} = $ 70,697
• Savings in IRA account will accumulate to an amount = FV (Rate, period, PMT) = FV(7%, 67 - 38, -17000) = $1,484,891
• PV of all the annuity of $ 100,000 required post retirement over 95 - 67 = 28 years = PV (Rate, period, PMT) = PV (7%, 28, -100000) = $ 1,213,711

Hence, total supply of money at retirement = 70,697 + 1,484,891 = $1,555,588 against a requirement of $ 1,213,711 towards retirement lifestyle.

Hence, both the requirements are met with the current savings or pattern of saving.