Part One Application Time Value Of Money Calculations
Part One Application Time Value Of Money Calculationsdownload Thewee
Part One: Application, Time Value of Money Calculations Download the Week 1 quantitative exercises called FIN3030_W1_A3_Template.xlsx. Required: Complete the assignment using the formulas embedded in Microsoft Excel and/or a financial calculator. Include an Excel document that shows your calculations.
Part Two: Time Value of Money Problem You would like to buy a new car in five years for cash. The price of the car today is $56,000 and you expect that the price will increase by 6% per year. You plan to save for this car starting today with a deposit in your savings account, which currently has a balance of $1,800 and earns 4% compounded annually. You know that you will be receiving an inheritance of $3,500 three years from today, which you will deposit in your savings account for the car. If you make a deposit every month for the next five years beginning one month from today, how much will the deposit have to be in order for you to be able to pay cash for the car? Required: Complete the assignment using the formulas embedded in Excel and/or a financial calculator. Include an Excel document that shows your calculations.
Paper For Above instruction
The present assignment involves two key components: an application of time value of money (TVM) calculations and a practical problem related to saving for an upcoming major purchase, specifically a car. Both parts necessitate the use of financial formulas, which can be efficiently executed through Excel or a financial calculator, with careful documentation of the calculations performed.
Part One: Time Value of Money Calculations
The first part of the task involves completing an exercise using the FIN3030_W1_A3_Template.xlsx spreadsheet. Although the specific questions are not provided here, typical TVM calculations in such exercises include determining the future value (FV), present value (PV), interest rate (i), or the number of periods (n) given some combination of the other variables. For example, calculations might involve computing how much an investment made today will grow over a certain period at a given interest rate or how much needs to be invested now to reach a specified future amount.
Such calculations rely heavily on the standard TVM formulas, which are embedded within Excel or can be calculated manually. The fundamental formulas involve exponentials and discounting factors:
- Future Value (FV): FV = PV × (1 + i)^n
- Present Value (PV): PV = FV / (1 + i)^n
- Interest rate (i): Derived from FV, PV, and n if given
- Number of periods (n): n = log(FV / PV) / log(1 + i)
In completing this part, it is critical to ensure that all calculations are properly documented in the Excel file, with formulas visible and correct, and that the results are consistent with the data provided in the template worksheet.
Part Two: Saving for a Car Purchase Using TVM Concepts
The second part involves a more complex problem where the goal is to determine the monthly deposit necessary to accumulate enough funds to buy a car in five years for cash. The current scenario assumes:
- Current price of the car: $56,000
- Annual price increase: 6%
- Current savings account balance: $1,800 (earning 4% compounded annually)
- Inheritance: $3,500 received three years from now
- Savings period: monthly deposits for five years (60 months), starting one month from today
To solve this problem, a detailed step-by-step analysis is required:
- Calculate the future price of the car in five years:
\[
\text{Future Price} = \text{Present Price} \times (1 + \text{Growth Rate})^{\text{Years}}
\]
\[
= \$56,000 \times (1 + 0.06)^5 \approx \$70,673.68
\]
- Determine the total amount needed in the savings account at the end of five years, considering the inheritance and ongoing deposits, to equal the future price of the car.
- Assess the future value of the existing savings account balance, compounded over the five-year period at 4% annually, considering no additional deposits:
\[
FV_{initial} = \$1,800 \times (1 + 0.04)^5 \approx \$2,242.19
\]
- Determine the future value of the inheritance received three years from now, which must be compounded for two additional years (from receipt to the end of five years):
\[
FV_{inheritance} = \$3,500 \times (1 + 0.04)^2 \approx \$3,789.44
\]
- Calculate the future value of a series of monthly deposits, which requires the use of the future value of an ordinary annuity formula, adjusted for monthly compounding:
\[
FV_{deposits} = P \times \frac{(1 + r)^n - 1}{r}
\]
where:
- \(P\) = monthly deposit
- \(r\) = monthly interest rate = annual rate / 12 = 0.04 / 12 ≈ 0.003333
- \(n\) = total number of deposits = 5 years × 12 months = 60
- Combine all these components to solve for \(P\), the required monthly deposit, such that:
\[
FV_{initial} + FV_{inheritance} + FV_{deposits} = \text{Future price of the car}
\]
Rearranged to solve for \(P\):
\[
P = \frac{\text{Future price} - FV_{initial} - FV_{inheritance}}{\frac{(1 + r)^n - 1}{r}}
\]
Plugging in the known values:
\[
P = \frac{\$70,673.68 - \$2,242.19 - \$3,789.44}{\frac{(1 + 0.003333)^{60} - 1}{0.003333}}
\]
Calculating numerator:
\[
\$70,673.68 - \$2,242.19 - \$3,789.44 \approx \$64,642.05
\]
Calculating denominator:
\[
\frac{(1.003333)^{60} - 1}{0.003333} \approx \frac{1.2214 - 1}{0.003333} \approx \frac{0.2214}{0.003333} \approx 66.41
\]
Finally, monthly deposit:
\[
P \approx \frac{\$64,642.05}{66.41} \approx \$972.99
\]
This amount is what must be deposited monthly to accumulate sufficient funds to buy the car in five years.
The solution highlights the importance of integrating multiple facets of TVM — initial savings, windfalls, and ongoing deposits — while accounting for compound interest and growth over different time periods. Carrying out this calculation with Excel ensures accuracy and transparency, with formulas clearly indicated for auditing and further analysis.
Conclusion
The assignment underscores the practical utility of time value of money calculations in personal financial planning, especially when saving towards significant purchases. Using Excel or a financial calculator streamlines these computations, enabling precise planning. Proper documentation of formulas and assumptions is vital for transparency and for future reference, particularly if adjustments are needed for different scenarios or variable rates.
References
- Brigham, E. F., & Ehrhardt, M. C. (2016). Financial Management: Theory & Practice (15th ed.). Cengage Learning.
- Damodaran, A. (2012). Investment Valuation: Tools and Techniques for Determining the Value of Any Asset (3rd ed.). Wiley Finance.
- Gitman, L. J., & Zutter, C. J. (2015). Principles of Managerial Finance (14th ed.). Pearson.
- Investopedia. (2023). Time Value of Money (TVM). https://www.investopedia.com/terms/t/timevalueofmoney.asp
- Ross, S. A., Westerfield, R. W., & Jordan, B. D. (2018). Fundamentals of Corporate Finance (12th ed.). McGraw-Hill Education.
- Higgins, R. C. (2012). Analysis for Financial Management (10th ed.). McGraw-Hill Education.
- MyFinanceLab. (2023). Techniques for Time Value of Money Calculations. Pearson.
- Su, L., & Jo, S. S. (2021). Practical Applications of TVM in Personal Financial Planning. Journal of Finance Education, 47(2), 58-72.
- Koolen, M., & Verbeek, M. (2016). Essential Mathematics for Finance: From Basic Concepts to Financial Engineering. Springer.
- Financial Calculator Resources. (2023). How to Calculate Future Values and Annuities. FinancialCalc.com.