Today, your team meets with your clients $($a married couple$),$ who both turn $43$ today and will retire

together when they turn $67,$ to review the financial planning report that you prepare for them. Their

combined salary for the year that begins today is set at an annual rate of $($$$9,750*6\mathrm{.}67+$

$$75,000),$ being paid equally at the end of each month. Your clients expect an annual $3\%$ raise in

their salary $($i$.$e$.,$ once a year, not monthly$)$ until they retire. They deposit $12\%$ of their monthly

salary in their $401($k$)$ account that generates an annual rate of return of $8\mathrm{.}4\%,$ compounded daily.

And their employer matches their contribution with $3\mathrm{.}5\%$ of their salary to the same $401($k$)$ account. At the end of each year, your clients will receive a bonus set at $11\%$ of their annual salary. Your

clients commit to deposit $$12,500$ out of their annual bonus in a $529$ Plan account each year for

financing$/$subsidizing higher education costs of their daughter, who just turned $10$ yesterday. If

their annual bonus is less than $$12,500,$ they will deposit the entire annual bonus in the $529$ Plan

account, which generates an annual rate of return of $7\mathrm{.}02\%,$ compounded weekly. They will

contribute annually to the $529$ Plan account until their daughter finishes her $5-$year undergraduate

study. Any remaining amount from the annual bonus will be deposited in their $($traditional$)$ IRA

account, which has an annual compounded rate of return of $9\mathrm{.}5\%.$

Besides, your clients plan to celebrate their $60-$year birthday anniversary with an around$-$the$-$world

cruise. They will finance their cruise, which has a total cost of $$65,000$ for the couple, by

withdrawing the needed amount, which is subjected to $24\%$ tax rate, from their IRA account. If

there is insufficient fund in their IRA account to cover the full expenses of the cruise, they will

withdraw the entire balance at the time from their IRA account.

Q$3.$ Determine with precise explanation the cash flows pattern of their annual contributions to

the IRA account; and calculate their IRA account balance upon their retirement.

Today, annual college expenses are running at $$30,000,$ and are expected to grow at an annual rate

of $4\%.$ Their daughter will enter college when she turns $18$ and will complete her undergraduate

study in FIVE years. Your clients expect their daughter to be responsible for $30\%$ 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 to pay for their

share of their daughter$$s college expenses.

Q$4.$ Determine with precise explanation the cash flows pattern of their annual contributions to

the $529$ Plan account; and calculate and precisely explain your choice of interest rate, i$.$e$.,$

EAR$/$EPR$/$PER $($select the correct choice$),$ used in the analysis. Also, calculate the $529$

Plan account balance right before the first withdrawal to pay for their daughter$$s college

expenses.