1)You have just turned 30 years old, have just received your MBA, and have accepted your first job. Now you must decide how much money to put into your retirement plan. The plan works as follows: Every dollar in the plan earns 7% per year. You cannot make withdrawals until you retire on your sixty-fifth birthday. After that point, you can make withdrawals as you see fit. You decide that you will plan to live to 100 and work until you turn 65. You estimate that to live comfortably in retirement, you will need $100,000 per year starting at the end of the first year of retirement and ending on your one hundredth birthday. You will contribute the same amount to the plan at the end of every year that you work. How much do you need to contribute each year to fund your retirement?

2)Problem 1 is not so realistic because most retirement plans do not allow you to specify a fixed amount to contribute every year. Instead, you are required to specify a fixed percentage of your salary that you contribute. Assume that your starting salary is $750,000 per year and it will grow 2% per year until you retire. Assuming everything stays the same as in problem 45, what percentage of your income do you need to contribute to the plan every year to fund the same retirement income?

Problem 45 is not very realistic because most retirement plans do not allow you to specify a fixed amount to contribute every year. Instead, you are required to specify a fixed percentage of your salary that you want to contribute. Assume that your starting salary is 75,000 per year and it will grow 2% per year until you retire. Assuming everything else stays the same as in Problem 45, what percentage of your income do you need to contribute to the plan every year to fund the same retirement income?

1) Well, congratulations on reaching such a milestone and getting your MBA! Now, let's crunch some numbers to figure out how much you need to contribute each year. With a retirement age of 65 and an estimated lifespan of 100, you will need to fund 35 years of retirement (100 - 65 = 35).

To live comfortably in retirement, you need $100,000 per year from the end of the first year of retirement until your hundredth birthday. So, to calculate the total amount needed for those 35 years, multiply $100,000 by 35:

$100,000 * 35 = $3,500,000

Therefore, to fund your retirement, you will need to contribute a total of $3,500,000 over the course of your working years.

2) Ah, the complications of real life! In this case, let's consider your starting salary of $750,000 per year, which grows by 2% annually until you retire at 65. To figure out the percentage of your income you should contribute, we'll have to determine the total amount you'll earn over your working years.

To simplify things, let's assume that your salary grows linearly by 2% each year. This means that in the first year, you earn $750,000, in the second year, you earn $750,000 + 2% of $750,000, and so on.

To calculate the average salary over your working years, we'll use the formula for the average of an arithmetic series:

Average Salary = (Starting Salary + Ending Salary) / 2

The starting salary is $750,000, and the ending salary will be $750,000 * (1 + 0.02)^35 (assuming you work for 35 years). Now, let's plug these values into our formula:

Average Salary = ($750,000 + $750,000 * (1 + 0.02)^35) / 2

Now, to determine the percentage you need to contribute, divide the contribution needed ($3,500,000) by the average salary:

Percentage = ($3,500,000 / Average Salary) * 100

Now, go ahead and calculate these numbers to find out the percentage of your income you'll need to contribute annually to fund your desired retirement income!

1) To calculate the amount you need to contribute each year to fund your retirement, we can use the concept of present value. We need to determine the present value of the $100,000 annual retirement income for 35 years, starting at the end of the first year of retirement (age 65) and lasting until your one hundredth birthday (age 100).

First, let's calculate the present value factor using the given annual interest rate of 7%:

PV factor = 1 / (1 + interest rate)^number of years
PV factor = 1 / (1 + 0.07)^35
PV factor = 1 / 4.3219
PV factor ≈ 0.2310

Next, we can calculate the annual contribution needed to fund your retirement:

Annual contribution = Retirement income / PV factor
Annual contribution = $100,000 / 0.2310
Annual contribution ≈ $433,457

Therefore, you need to contribute approximately $433,457 each year to fund your retirement.

2) In this scenario, we need to determine the fixed percentage of your income that you need to contribute each year to fund the same retirement income.

First, let's calculate the ending salary at the time of retirement, considering a 2% annual salary growth:

Ending salary = Starting salary * (1 + salary growth rate)^number of years
Ending salary = $750,000 * (1 + 0.02)^35
Ending salary ≈ $1,270,203

Now, we can use the same present value calculation as before to determine the percentage of income to contribute:

PV factor = 1 / (1 + interest rate)^number of years
PV factor = 1 / (1 + 0.07)^35
PV factor = 1 / 4.3219
PV factor ≈ 0.2310

Percentage of income to contribute = (Retirement income / Ending salary) / PV factor
Percentage of income to contribute = ($100,000 / $1,270,203) / 0.2310
Percentage of income to contribute ≈ 0.3231

Therefore, you need to contribute approximately 32.31% of your annual income to the retirement plan each year to fund the same retirement income.

To answer both problems, we will use the concept of future value of annuity. An annuity is a series of equal cash flows made at regular intervals over a specified period of time. In this case, the cash flows represent the annual contributions to your retirement plan.

1) In problem 1, you need to calculate how much you need to contribute each year to fund your retirement. To do this, follow these steps:

Step 1: Calculate the number of years you will contribute to the plan. Since you plan to work until you turn 65 and then live until 100, the number of contribution years is 100 - 65 = 35 years.

Step 2: Determine the future value (FV) of your retirement fund. This is the amount you need to accumulate by the time you retire. Given that you'll need $100,000 per year during retirement, the total amount needed is $100,000 * 36 years (from end of first year of retirement to age 100) = $3,600,000.

Step 3: Use the future value of annuity formula to calculate the annual contribution needed. The formula is: A = (FV * r) / ((1 + r)^n - 1), where A is the annual contribution, FV is the future value, r is the interest rate per period, and n is the number of periods.

Plugging in the values, we have A = ($3,600,000 * 0.07) / ((1 + 0.07)^35 - 1). Evaluating this expression, we find that the annual contribution needed to fund your retirement is approximately $32,630.56.

2) In problem 2, you need to calculate the percentage of your income that you need to contribute to the plan every year. To do this, follow these steps, considering that your salary grows by 2% per year:

Step 1: Calculate the future value of your salary at retirement. Using the formula for the future value of a single sum, we have FV_salary = $750,000 * (1 + 0.02)^35 ≈ $1,424,186.89.

Step 2: Calculate the same future value as in problem 1, which is the amount needed to fund your retirement. We found in problem 1 that it is $3,600,000.

Step 3: Calculate the percentage of your income that you need to contribute each year. Divide the amount needed to fund your retirement by the future value of your salary and multiply by 100. This gives us ($3,600,000 / $1,424,186.89) * 100 ≈ 252.78%.

Therefore, you would need to contribute approximately 252.78% of your current salary each year to fund the same retirement income under the given assumptions. Note that this high percentage is due to the fact that your salary is growing faster (2%) than the interest rate on your retirement plan (7%).