Your clients, both just turned 42, will retire together when they turn 65. Today, they

have a combined salary at an annual rate of ($9,500*(5.33)salary scalar + $110,000), being paid

equally at the end of each month. They expect a 3% raise in their salary every year until

they retire. They deposit 10% of their monthly salary in their 401(k) account that

generates an annual rate of return of 9%, compounded daily. In addition, their employer

matches their contribution with 5% of their monthly salary to the same 401(k) account.

Q1. Determine the cash flows pattern of the monthly contributions to the 401(k)

account within each year; and calculate and explain precisely your choice of

interest rate, i.e., EAR/EPR/PER (select the correct choice), used in your analysis.

Also, calculate the year-end value of 401(k) contributions for each year. Verify

your work for Years 1 and 2 only with either the formula or the financial

calculator approach!

Q2. Determine the pattern of the year-end values of 401(k) contributions across years

(that you calculated for Q1); and calculate and explain precisely your choice of

interest rate, i.e., EAR/EPR/PER (select the correct choice), used in your analysis.

Also, calculate the 401(k) account balance upon their retirement. Verify your

work on the 401(k) account balance with the formula approach!

(Attention: Discuss with your teammates the difference between "year-end

values of 401(k) contributions" and "401(k) account balance"!!!)

At the end of each year, your clients will receive a bonus of 14% of their annual salary.

Your clients commit to deposit part of their annual bonus, $15,000, in a 529 Plan account

each year for financing the college education of their daughter's, who just turned 13.

They intend to contribute annually to the 529 account until their daughter finishes

college. Any remaining amount from the annual bonus check will be deposited in an IRA

account. The 529 Plan account and the IRA account are expected to generate annual

rates of return of 8% and 10%, respectively. And both accounts are compounded daily.

Q3. Determine the cash flows pattern of their contributions to the IRA account; and

calculate and explain precisely your choice of interest rate, i.e., EAR/EPR/PER

(select the correct choice), used in your analysis. Also, calculate their IRA

account balance upon their retirement.

Q4. Determine the cash flows pattern of their contributions to the 529 Plan account;

and calculate and explain precisely your choice of interest rate, i.e.,

EAR/EPR/PER (select the correct choice), used in your analysis. Also, calculate

the 529 Plan account balances at the time their child starts college. Verify your

work with either the formula or the financial calculator approach!

Today, annual college expenses are running at $35,000, and are expected to grow at an

annual rate of 4%. Their daughter will enter college when she turns 18, and complete the

degree program in five years. Your clients expect their daughter to be responsible for

25% of her college expenses by participating in the Federal Work-Study Program. All

annual college expenses will be due at the beginning of each year. Your clients will tap

into the 529 Plan account for paying their daughter's college expenses.

Q5. Will there be sufficient funding in the 529 account for financing their daughter's

college expenses? If not, when will the funding run out of money? Support

your answer numerically by showing the annual balances of the 529 Plan

account through their daughter's college years.

Anticipating a positive balance in the 529 account at their daughter's college graduation,

your clients will partially support her graduate study with money left in the 529 account.

Their daughter plans to work for three years before returning to graduate school for an

MBA. Today, annual expenses for a highly competitive full-time 2-year MBA program

are running at $54,000, and are expected to grow at an annual rate of 4%. Your clients

will offer assistance to their daughter's pursuit of graduate education through the 529

account at one-third of the annual expenses during her MBA study.

Q6. Will there be sufficient funding in the 529 account for subsidizing their daughter's

MBA program's expenses? If not, when will the funding run out of money?

Support your answer numerically numerically by showing the annual balances

of the 529 Plan account through her MBA study.

If there is money left (i.e., positive balance) in the 529 account after their daughter's

MBA study, your client will transfer the balance to their IRA account.

Q7. How large will be the nest egg upon the retirement of your clients? In other

words, calculate the combined balance of the 401(k) account and their IRA

account when they retire.

Upon their retirement, your clients will roll over their savings from both the 401(k)

account and the IRA account into a conservative account that is expected to generate an

annual rate of return of 6%, compounded monthly. Their retirement needs are expected

to be 90% of their salary right before their retirement, and are subject to monthly inflation

at an annual rate of 3%. Their combined social security benefits will cover 20% of their

retirement needs, and their pension benefits will cover another 5%. Your clients need to

withdraw from this conservative account at the beginning of each month in order to meet

the monthly expenses during their retirement horizon of 25 years.

Q8a. Determine the cash flows pattern of the withdrawals from the conservative

account; and calculate and explain precisely your choice of interest rate, i.e.,

EAR/EPR/PER (select the correct choice), used in your analysis. Will your

clients be able to leave any inheritance to their children at the end of their

retirement horizon? If so, calculate the size of the inheritance. If your clients

could not leave any inheritance to their children at the end of the retirement

horizon, at what age will they run out of money during their retirement? Support

your answer numerically.

Q8b. In order to help their children manage their money, your clients instruct you to

place the inheritance, i.e., the balance of the conservative account, in a trust fund

account, which distributes fixed quarterly payments to their children and their

offspring forever, at the end of their retirement horizon. The trust fund generates

an annual rate of return of 7.2%, compounded monthly. Determine the cash

flows pattern of the withdrawals from the trust fund account; and calculate and

explain precisely your choice of interest rate, i.e., EAR/EPR/PER (select the

correct choice), used in your analysis. Also, calculate the amount of the quarterly

payment.

Q8c. Alternatively, your clients give their daughter annually during their retirement

instead of leaving an inheritance at the end of their retirement horizon. Calculate

the maximum (fixed) amount of annual gift, and explain precisely your choice of

interest rate, i.e., EAR/EPR/PER (select the correct choice), used in your analysis.

Q9. Sensitivity of your analysis to the assumptions on the inflation rate and the rates

of return on retirement investment accounts. Other factors being equal,

(i) calculate the respective percentage changes in the nest egg (Q7), the

inheritance (Q8a), and the annual gift (Q8c), if the annual rate of returns

on the 401(k) account were 10%.

(ii) calculate the percentage change in the inheritance if the annual inflation

rate were 4%.