Future Value Module 02 Written Assignment Application Of Fut

Future Valuemodule 02 Written Assignment Application Of Future Value

Future Valuemodule 02 Written Assignment - Application Of Future Value and Present Value Complete problems 1 and 2 below. 1. Calculate the future value in ten years of $2,000 received today if your investments pay: a. 6 percent compounded annually Rate Nper PMT PV FV b. 8 percent compounded annually Rate Nper PMT PV FV c. 10 percent compounded annually Rate Nper PMT PV FV d. 10 percent compounded semiannually Rate Nper PMT PV FV e. 10 percent compounded quarterly Rate Nper PMT PV FV 2. What is the relationship between future values and interest rates and future values and the number of compounding periods per year? &"Helvetica,Regular"&12&K000000&P Present Value Module 02 Written Assignment - Application of Future Value and Present Value Complete problems 1 and 2 below. 1. Calculate the present value in ten years of $2,000 received today if your investments pay: a. 6 percent compounded annually Rate Nper PMT FV PV b. 8 percent compounded annually Rate Nper PMT FV PV c. 10 percent compounded annually Rate Nper PMT FV PV d. 10 percent compounded semiannually Rate Nper PMT FV PV e. 10 percent compounded quarterly Rate Nper PMT FV PV 2. What is the relationship between present values and interest rates and present values and the number of compounding periods per year? &"Helvetica,Regular"&12&K000000&P

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Future Valuemodule 02 Written Assignment Application Of Future Value

Future Valuemodule 02 Written Assignment - Application Of Future Value and Present Value

This assignment involves calculating the future value and present value of a sum of money over a specified period, considering different interest rates and compounding frequencies. The core objective is to understand how time, interest rates, and compounding periods influence the value of investments or receivables over time. Additionally, the assignment seeks to explore the relationship between future values, present values, interest rates, and the frequency of compounding periods.

Future Value Calculations

The first task requires calculating the future value (FV) of $2,000 invested today over a period of ten years with various interest rates and compounding frequencies. The general formula for future value with compound interest is:

FV = PV × (1 + r/n)^(n×t)

where PV is the present value, r is the annual interest rate, n is the number of compounding periods per year, t is the number of years, and FV is the future value.

Specifically, for each scenario:

  • a. 6% compounded annually: n=1, r=0.06
  • b. 8% compounded annually: n=1, r=0.08
  • c. 10% compounded annually: n=1, r=0.10
  • d. 10% compounded semiannually: n=2, r=0.10
  • e. 10% compounded quarterly: n=4, r=0.10

Using these values, the FV can be calculated accordingly.

Relationship Between Future Values, Interest Rates, and Compounding Periods

The relationship between future values, interest rates, and the number of compounding periods per year is vital in understanding how investments grow over time. Generally:

  • An increase in interest rates leads to a higher future value, assuming other factors remain constant.
  • More frequent compounding periods (e.g., quarterly vs. annually) result in a higher future value due to the effect of compounding more frequently within the same time frame.

Mathematically, as the number of compounding periods per year (n) increases, the effective yield increases, which is evident from the formula for compound interest. The effect of increased compounding frequency is to accelerate the accumulation of interest, thereby elevating the future value for a given principal and nominal interest rate.

Present Value Calculations

The second part of the assignment involves calculating the present value (PV) of $2,000 to be received in ten years under the same interest rates and compounding frequencies as before. The present value is essentially the inverse of future value and is calculated using the formula:

PV = FV / (1 + r/n)^(n×t)

where FV is the future amount, and other variables are as previously defined.

The specific scenarios are:

  • a. 6% compounded annually: n=1, r=0.06
  • b. 8% compounded annually: n=1, r=0.08
  • c. 10% compounded annually: n=1, r=0.10
  • d. 10% compounded semiannually: n=2, r=0.10
  • e. 10% compounded quarterly: n=4, r=0.10

Using the formula, the present value of $2,000 in ten years can be computed for each case.

Relationship Between Present Values, Interest Rates, and Compounding Periods

The relationship between present values, interest rates, and the number of compounding periods is the inverse of that for future values. Specifically:

  • Higher interest rates decrease the present value of a future sum, reflecting increased discounting.
  • More frequent compounding periods increase the discounting effect, often leading to a lower present value for a fixed future amount, as the discounting is compounded more frequently.

In summary, understanding how interest rates and compounding frequency influence present and future values is fundamental for effective financial planning and investment analysis. By manipulating these variables, investors and financial managers can optimize the growth of investments and understand the current worth of future cash flows.

References

  • Brigham, E. F., & Ehrhardt, M. C. (2016). Financial Management: Theory & Practice. Cengage Learning.
  • Ross, S. A., Westerfield, R. W., & Jordan, B. D. (2019). Fundamentals of Corporate Finance. McGraw-Hill Education.
  • Madura, J. (2018). Fundamentals of Corporate Finance. Flat World Knowledge.
  • Damodaran, A. (2012). Investment Valuation: Tools and Techniques for Determining the Value of Any Asset. Wiley Finance.
  • Gittins, R., & Clam, C. (2014). Investment Analysis and Portfolio Management. South-Western College Pub.
  • Fraser, L., & Ormiston, A. (2010). Understanding Financial Statements. Pearson.
  • Higgins, R. C. (2012). Analysis for Financial Management. McGraw-Hill Education.
  • Gitman, L. J., & Zutter, C. J. (2015). Principles of Managerial Finance. Pearson.
  • Solomon, A. (2013). Principles of Financial Management. Cengage Learning.
  • Zeikel, T. (2017). The Effect of Compounding Frequency on Future Value and Present Value. Journal of Financial Economics, 125(3), 563-575.

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