Homework Assignment Complete: The Problems Using An Excel Sp

Homeworkassignmentcomplete The Problems Using An Excel Spreadsheet P

Homeworkassignmentcomplete The Problems Using An Excel Spreadsheet P

Complete the problems using an Excel spreadsheet. Problem responses must contain all givens, equations, and the process in which the problem is solved.

1. State the present worth of the future payment of $9,450 five years from now at 7% compounded annually.

2. You have $7,450. You would really like that $7,450 to grow into $14,500 in the next five years so you can make a down payment on a new house. What compound interest rate would you need to receive to make your goal possible in five years?

3. Suppose you have the option of receiving either $6,500 at the end of six years or P dollars today. Currently, you have no need for the money, so you could deposit the P dollars into a bank account that pays 11% interest compounded annually. What value of P would make you indifferent in your choice between P dollars today and the promise of $6,500 at the end of six years?

4. State the total amount accumulated by a present investment of $9,000 in five years at 9% compounded annually.

5. Which of the following alternatives would you choose (having the highest value), assuming an interest rate of 10% compounded annually? a) Receive $2000 today. b) Receive $3500 three years from now. c) Receive $4000 six years from now.

6. You deposit $7,000 in a savings account that earns 9% simple interest per year. How many years will it take to double your balance? If, instead, you deposit the $7,000 in another savings account that earns 7% compounded yearly, how many years will it take to double your balance?

Paper For Above instruction

The following comprehensive analysis addresses each of the provided financial problems using Excel as the computational tool. Accurate application of financial formulas, including present value, future value, compound interest rate calculation, and simple interest calculations, will be demonstrated to ensure clarity and precision in solving each problem.

Problem 1: Present Worth of a Future Payment

Given a future sum of $9,450 due in five years with an annual interest rate of 7%, the present worth is calculated using the present value formula:

PV = FV / (1 + r)^n

Where FV = $9,450, r = 0.07, n = 5 years.

Calculating in Excel:

= annotated formula = 9450 / (1 + 0.07)^5

By inputting into Excel: =9450 / (1 + 0.07)^5, we obtain approximately $6,582.68.

This amount represents the current value equivalent of receiving $9,450 five years from now at a 7% annual interest rate.

Problem 2: Required Compound Interest Rate

To determine the interest rate needed for an investment of $7,450 to grow to $14,500 in five years, rearranged compound interest formula is used:

r = (FV / PV)^{1/n} - 1

In Excel: = (14500 / 7450)^(1/5) - 1

Computing yields:

= (14500 / 7450)^(1/5) - 1 ≈ 0.1264, or 12.64%.

Thus, an annual compound interest rate of approximately 12.64% is required to meet the goal in five years.

Problem 3: Indifference Valuation

The present value (P) of receiving $6,500 in six years, with an 11% interest rate, is computed as:

P = FV / (1 + r)^n

In Excel: = 6500 / (1 + 0.11)^6

Calculating yields:

= 6500 / (1 + 0.11)^6 ≈ 6500 / 1.8983 ≈ $3421.89

Therefore, depositing approximately $3,421.89 today at 11% interest makes you indifferent between receiving the lump sum now or $6,500 in six years.

Problem 4: Total Future Value

Investing $9,000 at 9% interest compounded annually over five years, the future value (FV) is:

FV = PV * (1 + r)^n

In Excel: = 9000 * (1 + 0.09)^5

This computes to:

= 9000  (1 + 0.09)^5 ≈ 9000  1.5386 ≈ $13,847.40

This is the total accumulated amount after five years.

Problem 5: Optimum Investment Choice

Option a): $2000 today, which has present value of $2000.

Option b): $3500 in three years; present value:

= 3500 / (1 + 0.10)^3 ≈ 3500 / 1.331 ≈ $2,628.50

Option c): $4000 in six years; present value:

= 4000 / (1 + 0.10)^6 ≈ 4000 / 1.7716 ≈ $2,259.04

Comparing the present values, the best choice is the $3500 at three years, with a present value of approximately $2,628.50.

Problem 6: Doubling Investment with Simple and Compound Interest

Using simple interest, the formula to double the principal is:

t = (F - P) / (P * r)

Where:

  • P = 7000
  • F = 14000
  • r = 0.09

Time:

= (14000 - 7000) / (7000 * 0.09) = 7000 / 630 ≈ 11.11 years

With simple interest, it takes approximately 11.11 years to double the balance.

Using compound interest, the formula to find the time to double is:

t = log(2) / log(1 + r)

For r = 0.07:

= log(2) / log(1 + 0.07) ≈ 0.6931 / 0.0677 ≈ 10.24 years

So, it will take approximately 10.24 years for the $7000 deposit to double at 7% compounded annually.

These calculations show the significant difference in time required based on the interest pattern.

Conclusion

The application of these fundamental financial formulas in Excel enables precise computation of present values, future values, required rates, and investment comparisons, essential for sound financial decision-making. Careful analysis indicates that the preferred choices depend on the specific calculations and the rate of return, demonstrating the importance of accurate financial modeling in personal and institutional finance.

References

  • Brigham, E. F., & Ehrhardt, M. C. (2016). Financial Management: Theory & Practice. Cengage Learning.
  • Damodaran, A. (2012). Investment Valuation: Tools and Techniques for Determining the Value of Any Asset. Wiley Finance.
  • Ross, S. A., Westerfield, R. W., & Jordan, B. D. (2019). Fundamentals of Corporate Finance. McGraw-Hill Education.
  • Shapiro, A. C. (2017). Multinational Financial Management. Wiley.
  • Investopedia. (2023). Present Value (PV): Definition and Calculation. Retrieved from https://www.investopedia.com/terms/p/presentvalue.asp
  • Investopedia. (2023). Future Value (FV): Definition and Calculation. Retrieved from https://www.investopedia.com/terms/f/futurevalue.asp
  • Khan Academy. (2021). Compound interest and exponential growth. Retrieved from https://www.khanacademy.org/economics-finance-domain/core-finance/interest-tutorial
  • Corporate Finance Institute. (2022). Time Value of Money (TVM). Retrieved from https://corporatefinanceinstitute.com/resources/knowledge/finance/time-value-of-money/
  • Money Control. (2023). Simple Interest and Compound Interest. Retrieved from https://www.moneycontrol.com/financial-literacy/financial-products/savings-account/simple-vs-compound-interest.html
  • Morningstar. (2023). Investment Decision-Making and Financial Metrics. Retrieved from https://www.morningstar.com

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