Here is the solution for 1,2 and 3

Q1: Cash Flows Pattern and Interest Rate for SEP IRA Account:

Cash Flows Pattern:

1. Initial semi-annual income = $15,000 * 4.6667 = $69,000.5
2. Contribution to the SEP IRA = 12% of $69,000.5 = $8,280.06

The income grows at 1.5% semi-annually, so for every subsequent 6-month period, the contribution to the SEP IRA will be: Contribution in period t = $8,280.06 * (1 + 1.5%)^t

Interest Rate Selection: Given the annual rate of return is 9.6% compounded monthly: EPR (Effective Periodic Rate for a month) = (1 + 0.096/12) = 1.008 EAR (Effective Annual Rate) = (1.008)^12 - 1 = 0.0999 or 9.99% Since we have semi-annual cash flows, the semi-annual rate or EPR for 6 months is: EPR (6 months) = (1.008)^6 - 1 = 0.0489 or 4.89%

This is the rate we'll use for discounting the semi-annual contributions to the SEP IRA.

SEP IRA Balance Calculation: Using the formula for future value of a growing annuity compounded differently than payments are made: FV=Prg((1+r)n(1+g)n)(1+r) Where: P = Initial payment (contribution) = $8,280.06 r = EPR for 6 months = 4.89% or 0.0489 g = growth rate = 1.5% or 0.015 n = number of periods = 2*(62-38) = 48 (because they're depositing for 24 years, semi-annually)

Future Value (FV) calculation for the SEP IRA account balance upon their retirement using the formula mentioned:

For clarity, let's define the terms:

• P is the initial payment or contribution, which is $8,280.06.
• r is the semi-annual EPR, which is 4.89% or 0.0489.
• g is the growth rate of the contribution, which is 1.5% or 0.015.
• n is the number of periods, which is 48 (they're depositing for 24 years, semi-annually).

Using the formula for future value of a growing annuity compounded differently than payments are made:

Plugging in the values:

FV = $8,280.06 \times \frac{((1 + 0.0489)^{48} - (1 + 0.015)^{48})}{0.0489 - 0.015} \times (1 + 0.0489)

Using a calculator or software:

FV = $8,280.06 \times \frac{(2.7571 - 1.9261)}{0.0339} \times 1.0489

FV = $8,280.06 \times 24.5235 \times 1.0489

FV = $205,561.53 \times 1.0489

FV \approx $215,836.48

So, the SEP IRA account balance upon their retirement will be approximately $215,836.48.

Remember, this is the total accumulated value in the SEP IRA from their contributions over 24 years. The value is based on assumptions and the data provided. Adjustments in any of the factors (like contribution, rate of return, etc.) will change this projected value.

Taxable Brokerage Account and 529 Plan:

Brokerage Account Contributions:

1. Contribution = 10% of $69,000.5 = $6,900.05

This grows similarly as the SEP IRA contribution, but for every subsequent 6-month period, the contribution to the brokerage account will be:

Contribution in period t = $6,900.05 * (1 + 1.5%)^t

Given the daily compounding at 9% annual return, we need to calculate the daily compounded rate and then find the semi-annual compounded rate similar to the method above.

529 Plan Contributions: They commit $12,000 annually, so they'll be withdrawing this amount from the brokerage account. Given that they will do this until their daughter finishes college (assuming 4-year college), they'll make 4 transfers.

55th Birthday Trip: They will withdraw $70,000 from the brokerage account on their 55th birthday, which is in 17 years.

Problem 2:

Cash Flows Pattern of the Semi-annual Contributions:

Given that the family income at the end of six months from today is $15,000 \times \text{income scalar} and this amount grows at 1.5% semi-annually, the sequence of their contributions will look as follows:

1=0.1215,000income scalarC1=0.1215,000income scalar 2=0.1215,000income scalar(1+0.015)C2=0.1215,000income scalar(1+0.015) 3=0.1215,000income scalar(1+0.015)2C3=0.1215,000income scalar(1+0.015)2 And so on...

2. Correct Choice of Interest Rate:

The interest rate given is an annual rate compounded monthly, which is the Annual Percentage Yield (APY) or Effective Annual Rate (EAR).

To convert the EAR to an equivalent semi-annual rate (since contributions are made semi-annually), we use the formula:

(1+EAR)=(1+EPR/2)2(1+EAR)=(1+EPR/2)2 Where EPR is the Effective Periodic Rate.

Given EAR = 9.6% or 0.096,

(1+0.096)=(1+EPR/2)2(1+0.096)=(1+EPR/2)2 1.096=(1+EPR/2)21.096=(1+EPR/2)2 EPR/2=1.0961EPR/2=1.0961

Upon solving, you get:

EPR/24.694EPR/24.694

Therefore, the semi-annual rate (EPR/2) you should use is approximately 4.694%.

3. Brokerage Account Balance Upon Retirement:

Now, determine how many semi-annual periods there will be from age 38 to age 62:

2(6238)=48 periods

The SEP IRA account grows at a semi-annual rate of 4.694%, and the couple contributes at the end of each semi-annual period. This is essentially a growing annuity problem.

The future value of a growing annuity can be calculated as:

FV=Crg(1+r)n(1+g)n

Where: C = Initial contribution = 0.1215,000income scalar0.1215,000income scalar r = Semi-annual interest rate = 4.694% or 0.04694 g = Growth rate of income = 1.5% or 0.015 n = Number of periods = 48

Substitute the values into the formula to get the future value for each contribution and sum them up to get the total brokerage account balance upon retirement.

However, given the complexity of this formula when considering the growth of contributions, it's typically easier and more precise to use financial calculator tools or software for these calculations.

Problem 3:

1. Cash Flows Pattern for the 529 Plan Account: Given their daughter is 10 years old now and will enter college at 18, they have 8 years to contribute to the 529 Plan. You need to determine the annual contribution required to cover their share of her college expenses.

2. Choice of Interest Rate: For an annual compounding rate, the correct choice of interest rate for analysis is the Effective Annual Rate (EAR). If the account compounds more frequently than annually (e.g., monthly or quarterly), you would adjust the rate to the equivalent EAR for analysis. The problem doesn't specify the rate or the compounding frequency for the 529 Plan account, so I'll assume an average annual return rate for such accounts, say 6% compounded annually, for this illustration. (If you have a specific rate and compounding frequency, please provide it.)

3. 529 Plan Account Balance:

Let's use the future value of an ordinary annuity formula to calculate the balance at the start of college:FV=P(r(1+r)n1)

Where:

• P = Annual contribution (which we need to find out)
• r = Annual interest rate (6% or 0.06 in decimal form, assuming the average return rate)
• n = Number of years (8 years in this case)

4. College Expenses Calculation:

Annual college expenses today = $35,000

In 8 years, considering a 3% annual growth rate:

Future College Expense = $35,000 \times (1 + 0.03)^8 = $35,000 \times 1.26677 = $44,337

Given the daughter will cover 25% of this through the Federal Work-Study Program:

=75ParentsShare=75 = $33,252.75

o calculate the Future Value (FV), we'll be using the formula:

FV=P(r(1+r)n1)

Where:

• P = Annual contribution
• r = Annual interest rate
• n = Number of years

From the information you provided:

• r (Annual interest rate) = I'm assuming 6% based on the average return rate for 529 plans unless otherwise stated. So r = 0.06.
• n (Number of years) = 8 years, given she will start college at 18 and she's currently 10.

Future College Expense Calculation:

Annual college expenses today = $35,000

In 8 years, considering a 3% annual growth rate:

Future College Expense = $35,000 \times (1 + 0.03)^8 = $35,000 \times 1.26677 = $44,337

Given the daughter will cover 25% of this:

=75ParentsShareforthefirstyear=75 = $33,252.75

This is the expected expense for the first year. However, she will be in college for 5 years, and each year the expense is expected to grow at 3%.

1st Year: Future College Expense = $35,000 \times (1 + 0.03)^8 = $35,000 \times 1.26677 = $44,337

2nd Year: = $44,337 \times 1.03 = $45,667

3rd Year: = $45,667 \times 1.03 = $47,037

4th Year: = $47,037 \times 1.03 = $48,448

5th Year: = $48,448 \times 1.03 = $49,901

Step 2: Calculate Parents' Share of the College Expenses

Parents cover 75% of the expenses each year:

1st Year: $33,252.75 2nd Year: $34,250.25 3rd Year: $35,277.75 4th Year: $36,336.00 5th Year: $37,425.75

Now, you need sum these up to get the total expense over the five years:

Total Expense = $33,252.75 + $34,250.25 + $35,277.75 + $36,336.00 + $37,425.75 Total Expense = $176,542.50

Step 3: Calculate the Future Value of the 529 Plan Contributions

Using the Future Value of an annuity formula:

)FV=P(r(1+r)n1)

Where:

• P = Annual contribution (unknown)
• r = 0.06 (6% annual return)
• n = 8 years

Rearranging for)P=(r(1+r)n1)FV

Plugging in the known values, FV = $176,542.50, =0.06r=0.06, and =8n=8:

=176,542.50((1+0.06)810.06)P=(0.06(1+0.06)81)176,542.50=176,542.5011.7171P=11.7171176,542.50P = $15,078.47

Can somebody provide solution for 4,5 and 6 as soon as possible

8 , then the income scalar for the team will be (0+6+8)/3=4.6667. If the team's income scalar is 4.0 or less, add 3.8 to the calculated value and use it as the income scalar in your analysis. Assume 360-day year and 30-day month in your analysis. Your clients (a married couple), both turn 38 today, have diligently run their family business for 12 years and have paid off all of their debts. Recently, their business has grown into a stable stage that generates a growing income stream for the family. From your initial consultation with your clients, you learn that they plan to retire on the day they turn 62 . Their family income is $15,000incomescalar at the end of six months from today, and they expect their family income will grow at a steady rate of 1.5% semi-annually until they retire. To prepare for retirement, your clients deposit 12% of their semi-annual income in a taxdeferred SEP IRA account that generates an annual rate of return of 9.6%, compounded monthly. Q1. Determine (with precise explanation) the cash flows pattern of the semi-annual contributions to the SEP IRA account; and calculate and precisely explain the correct choice of interest rate, i.e., EAR/EPR/PER, that you should use in the analysis. Also, calculate the SEP IRA account balance upon their retirement. Then, verify your work on the SEP IRA account balance with the formula approach (that is presented in the lecture materials) in the report! In addition to their retirement savings, your clients contribute 10% of their semi-annual income into a taxable brokerage account that generates an annual after-tax return of 9%, compounded daily, to cover their financial needs before their retirement. Starting this year, your clients commit to help finance their ten-year old daughter's college education by transferring $12,000 from the brokerage account to a 529 Plan account at the end of each year. Your clients will transfer fund annually to the 529 Plan account until their daughter finishes college. The 529 Plan account is expected to generate an annual rate of return of 7.2%, compounded monthly. Besides, your clients plan to celebrate their 55-year birthday anniversary with an around-theworld cruise for a total cost of $70,000. They will finance these trips with their savings in the brokerage account. Any remaining balance in their brokerage account will supplement the SEP IRA account for financing their retirement. Q2. Determine (with precise explanation) the cash flows pattern of the semi-annual contributions to the brokerage account; and calculate and precisely explain the correct choice of interest rate, i.e., EAR/EPR/PER, that you should use in the analysis. Also, calculate the brokerage account balance upon their retirement. Q3. Determine (with precise explanation) the cash flows pattern of the annual fund transfers to the 529 Plan account; and calculate and precisely explain the correct choice of interest rate, i.e., EAR/EPR/PER, that you should use in the analysis. Also, calculate the 529 Plan account balance (right before the first withdrawal for college tuition) at the time their daughter starts college. Then, verify your work on the 529 Plan account balance with either the formula or the financial calculator approach (that is presented in the lecture materials) in the report! Today, annual college expenses are running at $35,000, and are expected to grow at an annual rate of 3%. Their daughter, who just turned 10 , will enter college when she turns 18 , and complete her undergraduate study 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 share of their daughter's college expenses. Q4. Will there be sufficient fund in the 529 Plan account to finance their daughter's college expenses? If not, when will the 529 Plan account run out of money? Support your answer numerically by showing the annual balances of the 529 Plan account through their daughter's college years. If there is a positive balance in the 529 Plan account at their daughter's college graduation, your clients will partially support her graduate study with money left in the 529 Plan account. Their daughter plans to work for THREE years before returning to graduate school for an MBA. Today, annual expenses for a competitive full-time 2-year MBA program are running at $58,000, and are expected to grow at an annual rate of 3.3%. Your clients will want to offer assistance to their daughter's pursuit of graduate education with available fund (if any) in the 529 Plan account by subsidizing one-fifth of the annual expenses during her MBA study. If there is a positive balance in the 529 Plan after subsidizing their daughter's 2-year MBA study, the remaining balance will be added to their brokerage account. Q5. Will there be sufficient fund in the 529 Plan account for subsidizing their daughter's MBA program's expenses? If not, when will the 529 Plan account run out of money? Support your answer numerically numerically by showing the annual balances of the 529 Plan account through their daughter's MBA study. Upon their retirement, your clients will roll over the entire balance of their SEP IRA account into the Roth IRA account by paying a 24% tax rate on the balance upon conversion. Q6. How large will be the after-tax nest egg upon the retirement of your clients? In other words, calculate the combined balance of the Roth IRA account and their brokerage account as they start enjoying their retirement. Also, offer THREE distinctively different recommendations (with precise explanations) to your clients that could increase their nest egg. 8 , then the income scalar for the team will be (0+6+8)/3=4.6667. If the team's income scalar is 4.0 or less, add 3.8 to the calculated value and use it as the income scalar in your analysis. Assume 360-day year and 30-day month in your analysis. Your clients (a married couple), both turn 38 today, have diligently run their family business for 12 years and have paid off all of their debts. Recently, their business has grown into a stable stage that generates a growing income stream for the family. From your initial consultation with your clients, you learn that they plan to retire on the day they turn 62 . Their family income is $15,000incomescalar at the end of six months from today, and they expect their family income will grow at a steady rate of 1.5% semi-annually until they retire. To prepare for retirement, your clients deposit 12% of their semi-annual income in a taxdeferred SEP IRA account that generates an annual rate of return of 9.6%, compounded monthly. Q1. Determine (with precise explanation) the cash flows pattern of the semi-annual contributions to the SEP IRA account; and calculate and precisely explain the correct choice of interest rate, i.e., EAR/EPR/PER, that you should use in the analysis. Also, calculate the SEP IRA account balance upon their retirement. Then, verify your work on the SEP IRA account balance with the formula approach (that is presented in the lecture materials) in the report! In addition to their retirement savings, your clients contribute 10% of their semi-annual income into a taxable brokerage account that generates an annual after-tax return of 9%, compounded daily, to cover their financial needs before their retirement. Starting this year, your clients commit to help finance their ten-year old daughter's college education by transferring $12,000 from the brokerage account to a 529 Plan account at the end of each year. Your clients will transfer fund annually to the 529 Plan account until their daughter finishes college. The 529 Plan account is expected to generate an annual rate of return of 7.2%, compounded monthly. Besides, your clients plan to celebrate their 55-year birthday anniversary with an around-theworld cruise for a total cost of $70,000. They will finance these trips with their savings in the brokerage account. Any remaining balance in their brokerage account will supplement the SEP IRA account for financing their retirement. Q2. Determine (with precise explanation) the cash flows pattern of the semi-annual contributions to the brokerage account; and calculate and precisely explain the correct choice of interest rate, i.e., EAR/EPR/PER, that you should use in the analysis. Also, calculate the brokerage account balance upon their retirement. Q3. Determine (with precise explanation) the cash flows pattern of the annual fund transfers to the 529 Plan account; and calculate and precisely explain the correct choice of interest rate, i.e., EAR/EPR/PER, that you should use in the analysis. Also, calculate the 529 Plan account balance (right before the first withdrawal for college tuition) at the time their daughter starts college. Then, verify your work on the 529 Plan account balance with either the formula or the financial calculator approach (that is presented in the lecture materials) in the report! Today, annual college expenses are running at $35,000, and are expected to grow at an annual rate of 3%. Their daughter, who just turned 10 , will enter college when she turns 18 , and complete her undergraduate study 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 share of their daughter's college expenses. Q4. Will there be sufficient fund in the 529 Plan account to finance their daughter's college expenses? If not, when will the 529 Plan account run out of money? Support your answer numerically by showing the annual balances of the 529 Plan account through their daughter's college years. If there is a positive balance in the 529 Plan account at their daughter's college graduation, your clients will partially support her graduate study with money left in the 529 Plan account. Their daughter plans to work for THREE years before returning to graduate school for an MBA. Today, annual expenses for a competitive full-time 2-year MBA program are running at $58,000, and are expected to grow at an annual rate of 3.3%. Your clients will want to offer assistance to their daughter's pursuit of graduate education with available fund (if any) in the 529 Plan account by subsidizing one-fifth of the annual expenses during her MBA study. If there is a positive balance in the 529 Plan after subsidizing their daughter's 2-year MBA study, the remaining balance will be added to their brokerage account. Q5. Will there be sufficient fund in the 529 Plan account for subsidizing their daughter's MBA program's expenses? If not, when will the 529 Plan account run out of money? Support your answer numerically numerically by showing the annual balances of the 529 Plan account through their daughter's MBA study. Upon their retirement, your clients will roll over the entire balance of their SEP IRA account into the Roth IRA account by paying a 24% tax rate on the balance upon conversion. Q6. How large will be the after-tax nest egg upon the retirement of your clients? In other words, calculate the combined balance of the Roth IRA account and their brokerage account as they start enjoying their retirement. Also, offer THREE distinctively different recommendations (with precise explanations) to your clients that could increase their nest egg