Week 4 Problem: Time Value Of Money - Use Excel Functions

Week 4problem Assignment Time Value Of Moneyuse Excel Functions To Co

Week 4 Problem Assignment: Time Value of Money Use Excel Functions to correctly calculate answers to all problems below. Explain in words what you do to make each calculation. Explain in words what the answers mean. In problems with an A and B part, explain what you learn from the difference. Use Excel functions such as FV, PV, NPER, RATE, and PMT to perform the calculations. For each problem, describe the steps taken and interpret the results. When comparing answers in parts a and b, analyze the differences and what insights they provide about the financial scenarios.

Paper For Above instruction

The Time Value of Money (TVM) is a fundamental concept in finance that recognizes the present value of money differs from its future value due to interest rates, inflation, and opportunity costs. Mastery of Excel functions such as FV, PV, NPER, RATE, and PMT is essential for accurate financial analysis involving investments, loans, annuities, and other cash flow scenarios. This paper discusses how to apply these functions to various typical financial problems, explains the implications of the results, and highlights key learnings from comparative analyses.

To illustrate the practical use of Excel in financial calculations, we consider multiple scenarios involving present and future values, loan amortizations, investment growth, and other related calculations.

1. Future Value of a Present Investment

Suppose an individual deposits $15,000 today with an annual interest rate of 1%. To determine the accumulated amount after 8 years, we use the FV function in Excel: =FV(rate, nper, pmt, pv). Since there are no additional payments, pmt is zero. Setting rate to 1%, nper to 8, and pv to -15000 (using negative for cash outflows), the calculation yields approximately $16,242.85. The positive result indicates how much the initial deposit will grow over 8 years with the specified interest rate. This demonstrates the power of compound interest to increase an investment over time.

2. Present Value of a Future Gift

Melanie is expected to receive a $7,000 gift in 4 years. With a discount rate of 3%, the present value (PV) can be calculated using the PV function: =PV(rate, nper, pmt, fv). Here, fv is $7,000, rate is 3%, and nper is 4. The calculated PV is approximately $6,219.41. This amount reflects what the future gift is worth today, accounting for the time value of money. Understanding PV helps in evaluating whether future sums are worth accepting now or whether alternative investments could yield better returns.

3. Valuation of Annuities

June will receive an annual annuity of $15,000 for 30 years, with a current long-term interest rate of 2.2%. Using the PV function for an ordinary annuity, the present value is calculated as: PV = PMT * [(1 - (1 + r)^-n) / r], where PMT is $15,000, r is 2.2%, and n is 30. If interest rates rise to 6%, the PV adjusts according to the new rate, impacting the present worth of future cash flows. These calculations underline how discount rates influence the valuation of long-term income streams and assist in making informed decisions about investments or retirement planning.

4. Loan Amortization and Loan Duration

Vinod invests $3,000 in a 20-year Treasury bond with a current interest rate of 2.25%. To find how long it takes to double or triple the investment, the logarithmic relationship can be used: time to double = log(2) / log(1 + r). At 2.25%, it takes approximately 31.15 years to double the money. Similarly, to triple, substitute 3 into the equation. Understanding these durations helps investors plan their contributions and evaluate the potential growth of fixed-income investments over different periods.

5. Mortgage Payments and Loan Planning

The Woods plan to buy a house with a $50,000 down payment and a $250,000 mortgage at 3% interest over 30 years. Calculating the monthly payment involves the PMT function: =PMT(rate/12, nper*12, -loan_amount). The result informs them of their monthly financial obligation, aiding in budgeting and mortgage qualification. Comparing different loan terms and interest rates enables strategic decision-making for home financing.

6. Retirement Savings and Compound Growth

Kim deposits $400 monthly into her retirement account, accumulating $500,000 over 30 years. To compute the average annual interest rate earned, the future value formula rearranged for rate is used: =RATE(nper, pmt, pv, fv). The calculated average interest rate, accounting for monthly compounding, indicates the effectiveness of her consistent contributions. Similarly, for possible lower returns of 6%, the future value can be recalculated to assess the impact of market performance assumptions.

7. Historical Growth Rates and Investment Analysis

Revenues of Walmart grew from $165 billion in 2000 to $485 billion in 2015. The compound annual growth rate (CAGR) can be calculated using: CAGR = (FV / PV)^(1/n) - 1. The result shows an average growth rate of approximately 7.45%, providing insight into the company's expansion over 15 years. This analysis aids investors and stakeholders in understanding long-term growth patterns and making projections.

8. Cost Analysis of Car Buying Options

James and Corrine compare leasing versus buying a car. The lease involves a $324 monthly payment for 3 years with an option to buy for $25,000, whereas purchasing involves different financing options. To evaluate the lowest cost, the present value of each option is calculated using the appropriate discount rate of 6% (monthly rate ≈ 0.5%). For the lease, the PV of all payments plus residual value is computed. For loan options, the calculation includes the monthly payments over the loan term. These analyses help in selecting cost-effective vehicle financing strategies, considering both short-term and long-term implications.

9. Investment Growth over Time

Bola invests in her retirement plan, contributing $9,000 annually for 25 years. Assuming a 12% annual return with compounding, the future value is derived from the FV function. At 12%, she would accumulate a substantial nest egg, indicating the benefits of high-yield investments over long periods. Conversely, at a conservative 6%, the total wealth would be considerably less, illustrating the importance of expected return assumptions in planning.

10. Impact of Changing Interest Rates and Investment Assumptions

Throughout the scenarios, changes in interest rates significantly affect the present value and future value calculations. For instance, a lower projected return of 6% reflects more conservative growth, impacting retirement savings and project evaluations. These variations emphasize the importance of accurate rate assumptions for realistic financial planning and decision-making.

Conclusion

Applying Excel functions to various financial problems enables precise calculations essential for making informed personal and institutional financial decisions. Understanding the underlying principles and interpreting the results in context allows better planning for investments, loans, retirement, and major purchases. Comparing different options, considering interest rate fluctuations, and analyzing the time value of money are central to effective financial management. The knowledge gained from these calculations fosters critical thinking and strategic decision-making, beneficial for individuals and organizations alike.

References

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