Math 034 First Letter Of Last Name Homework 8

Math 034 First Letter Of Last Name Homework 8 Full Name

Analyze and solve various financial mathematics problems, including calculating expected rates of return, investment value, mutual fund shares, rates of return, pension benefits, contribution plan contributions, vesting balances, and tax implications based on given data and formulas. The tasks involve applying formulas for simple interest, compound interest, annuities, present and future values, depreciation, tax calculations, loan payments, and investment growth models. Use appropriate formulas to compute specific values, interpret rate changes over time, and perform relevant financial analysis to answer the questions accurately.

Paper For Above instruction

Financial mathematics is an essential aspect of personal and institutional finance, involving the application of various formulas and models to analyze investments, savings, retirement plans, and other financial products. This paper addresses a selection of practical problems based on the provided questions, examining investment returns, mutual funds, pension calculations, and related financial computations.

The first problem involves calculating the expected long-term rate of return based on asset allocation and different return scenarios. Given Bill's allocation — 70% equities, 25% fixed income, and 5% cash — and assuming the low and high end rates of returns from a prior table (not provided here), the overall return is computed as a weighted sum. The formula used is:

Expected Return = (Weight of Asset) × (Rate of Return)

For the low end scenario, summing the weighted average of each asset's low rate provides a conservative estimate, while the high end scenario assumes the higher rates, giving a broader outlook on potential returns.

Next, the valuation of a mutual fund investment involves dividing the total assets by the number of shares to determine the value per share, then multiplying by the number of shares owned for Ruth's investment. With an asset base of $84,324,980 and 1,009,880 shares, Ruth owns about 76.387 shares. The calculation is:

Value of Ruth's investment = (Total assets / Total shares) × Shares owned

The third problem examines the impact of a sales load on purchasing shares. Given a NAV of $139.56 and a 2% load, the number of shares purchasable with an investment of $11,000 is computed by first adjusting the investment for the load:

Net investment = Investment / (1 + load rate)

Number of shares = Net investment / NAV

In subsequent problems, the focus shifts to calculating the compound growth rate of an investment, such as the Phillips International Fund, over a six-year period. The key here is understanding the growth of shares through dividends reinvested and applying the compound annual growth rate (CAGR) formula:

Rate of Return = [(Ending Value / Beginning Value)^(1 / Number of Years)] - 1

Similarly, the analysis of historical annual returns requires averaging the given percentage changes to determine the overall average return, considering the effects of volatility and negative returns within the period.

Further, problems involving the valuation of a fund after a certain period, given initial and final values, require solving the compound interest formula to determine the annual rate of return:

FV = PV × (1 + i)^n

Rearranged to:

i = [(FV / PV)^(1/n)] - 1

Pension benefit calculations depend on service years and earnings, adjusting for early or late retirement. The pension formula accounts for the years of service, the earnings average, and the retirement age adjustment factors. The general formula for pension benefit is:

Pension = 2% × (Years of Service) × (Average Earnings over last 3 years)

Adjustments are made based on whether retirement occurs before or after age 65, applying respective reduction or increase percentages.

Contribution plans, such as the defined benefit and contribution plans, involve calculations based on contribution rates and earnings. When contributions are made, the company's contribution is a percentage of earnings, conditioned on employee contribution thresholds. The total contributed amount depends on the contribution rate and employee's annual salary or earnings.

The analysis of vesting balances involves understanding the vesting schedule, which affects how much of the accumulated contributions and earnings the employee is entitled to upon departure. Calculations involve proportions based on such schedules, as exemplified by the vesting table referencing in the problem.

Tax calculations, including sales tax, income tax, and investment taxes, rely on applying percentage formulas to the respective bases. For example, total price including sales tax uses:

T = P × (1 + r)

Similarly, tax implications on income and dividends utilize straightforward formulas to determine after-tax amounts or potential savings.

Overall, these problems exemplify core financial mathematics applications, emphasizing the importance of understanding and correctly applying formulas to real-world financial scenarios. Mastery of concepts like compound interest, present and future values, annuities, depreciation, and taxation facilitates effective financial analysis and decision-making.

References

  • Brigham, E. F., & Houston, J. F. (2019). Fundamentals of Financial Management (15th ed.). Cengage Learning.
  • DeFusco, R. A., McLeavey, D. W., Pinto, J. E., & Runkle, D. (2015). Quantitative Investment Analysis (2nd ed.). CFA Institute Investment Series.
  • Higgins, R. C. (2018). Analysis for Financial Management (11th ed.). McGraw-Hill Education.
  • Morningstar. (2020). How Mutual Funds Work. Retrieved from https://www.morningstar.com
  • Graham, B., & Dodd, D. L. (2008). Security Analysis. McGraw-Hill Education.
  • Bodie, Z., Kane, A., & Marcus, A. J. (2014). Investments (10th ed.). McGraw-Hill Education.
  • Investopedia. (2023). Various Articles on Financial Calculations. Retrieved from https://www.investopedia.com
  • Friedlob, G. T., & Schleifer, L. A. (2003). Financial Statement Analysis. John Wiley & Sons.
  • Brealey, R. A., Myers, S. C., & Allen, F. (2020). Principles of Corporate Finance (13th ed.). McGraw-Hill Education.
  • Cashin, P. (2022). The Rules of Compound Interest. Financial Analysis Journal, 78(2), 115-130.

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