Challenge Problem Today: Is Your Birthday And You Are Now 37

Challenge Problemtoday Is Your Birthday And You Are Now 37 You A

Challenge Problem: Today is your birthday and you are now 37! You are planning your retirement and have decided that you can save $8,000.00 per year to go toward your retirement. The plan is to make your first deposit one year from today. You found a mutual fund that is expected to provide a return of 7.5% per year. You plan to retire at the age of 65, exactly 28 years from today. It is your expectation that you will live for 25 years after your retirement. Under these assumptions, how much can you spend each year after you retire? Your first withdrawal will be made at the end of your first retirement year. I'd like to get this in Excel with an explanation of how it works.

Distinguished Scholar Project: In order to illustrate the concept of the time value of money, let's consider the following scenario. Mary has decided to borrow $120,000. The terms of the loan are 6% over the next 4 years. She will be making annual payments (not monthly). This is an important distinction. Construct a loan amortization schedule that shows the 4 payments of Mary’s loan. Again, I'd like this solution in Excel with explanations.

Paper For Above instruction

The scenario presented involves crucial financial principles such as the future value (FV), present value (PV), annuities, and loan amortization, which are essential for understanding personal finance and investment planning. This paper discusses how to approach these calculations using Excel, which offers a powerful platform for performing financial computations, visualize cash flow schedules, and derive meaningful insights into long-term financial planning.

Retirement Savings and Withdrawal Calculations

The first challenge concerns estimating how much one can withdraw annually during retirement, based on current savings and expected investment returns. Given the details, an individual plans to save $8,000 annually, starting one year from today, in a mutual fund that yields a 7.5% annual return. The goal is to determine the annual withdrawal amount starting at retirement age 65, which occurs after 28 years, and for 25 years thereafter.

To find the amount available to spend annually post-retirement, we must first calculate the future value (FV) of the accumulated savings at retirement. This involves computing the future value of an ordinary annuity, which accounts for regular annual deposits and compound interest. The FV formula for an ordinary annuity in Excel is given by the RATE and NPER functions or the FV function directly.

The formula:

=FV(rate, nper, pmt, [pv], [type])

Where:

  • rate = 7.5% (0.075)
  • nper = 28 (years until retirement)
  • pmt = -8,000 (annual contribution, negative because it's an outflow)
  • pv = 0 (initial amount is zero)
  • type = 0 (payment at period end)

Calculating in Excel:

=FV(0.075, 28, -8000, 0, 0)

This yields the total amount saved at retirement. Subsequently, to determine the annual withdrawal, a common approach is to treat this accumulated amount as a present value of an annuity that pays out over 25 years with a 7.5% interest rate, representing the rate of return during retirement.

The formula for the annual withdrawal:

=PMT(rate, nper, pv, [fv], [type])

Parameters:

  • rate = 7.5% (0.075)
  • nper = 25
  • pv = the FV computed above (positive number representing the amount available at retirement)
  • fv = 0 (we aim to fully deplete the amount over 25 years)
  • type = 0 (withdrawals at end of each period)

In Excel:

=PMT(0.075, 25, -FV value, 0, 0)

This will output the annual amount you can withdraw for 25 years, assuming the investment continues to earn 7.5% during the withdrawal phase.

Loan Amortization Schedule

The second part involves creating an amortization schedule for a $120,000 loan at 6% annual interest over 4 years, with annual payments. The goal is to determine the fixed annual payment and break down each year's interest and principal components.

To compute the annual payment, we use the PMT function:

=PMT(rate, nper, pv)

Where:

  • rate = 6% (0.06)
  • nper = 4 years
  • pv = -120,000 (loan amount, as cash outflow)

Calculating in Excel:

=PMT(0.06, 4, -120000)

This provides the annual payment required to amortize the loan. To construct the schedule, for each year, you calculate:

  • Interest expense = remaining balance * interest rate
  • Principal repayment = total payment - interest expense
  • Remaining balance = previous balance - principal repayment

Using Excel, formulas are:

=Previous Balance * 0.06
=Payment - Interest Expense
=Previous Balance - Principal Repayment

This process continues for each of the four years, providing a detailed schedule showing how payments cover interest and reduce principal over time.

Conclusions and Practical Implications

Applying these calculations through Excel helps individuals understand how to plan for retirement efficiently and manage debt responsibly. The key takeaways include the importance of consistent savings, the power of compound interest, and the structured approach to loan repayment. These financial tools enable better decision-making, allowing for strategic planning aligned with long-term objectives.

References

  • Brigham, E. F., & Ehrhardt, M. C. (2016). Financial Management: Theory & Practice (15th ed.). Cengage Learning.
  • Ross, S. A., Westerfield, R. W., & Jordan, B. D. (2018). Essentials of Corporate Finance (10th ed.). McGraw-Hill Education.
  • Investopedia. (2023). "Future Value of an Annuity." Retrieved from https://www.investopedia.com/terms/f/future_value_annuity.asp
  • MyFinancialCellar. (2022). "Loan Amortization Schedule Calculator." Retrieved from https://myfinancialcellar.com/loan-amortization-schedule
  • SmartAsset. (2023). "How to Calculate Retirement Savings." Retrieved from https://smartasset.com/retirement/retirement-calculator
  • Avery, S., & Friedman, M. (2015). Personal Finance Essentials. Pearson.
  • California State University, Sacramento. (2020). "Present and Future Value Calculations." Retrieved from https://csus.edu/
  • Federal Reserve. (2022). "Interest Rates and Economic Outlook." Retrieved from https://federalreserve.gov
  • Fidelity Investments. (2023). "Retirement Planning Strategies." Retrieved from https://fidelity.com/retirement
  • Tax Guide. (2022). "Understanding Loan Amortization." Journal of Financial Planning, 35(4), 45–52.

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