Convert Between Percentages And Decimal Form ✓ Solved

Convert Between Percentages And Decimal Formconvert Time Periods To Y

Convert between percentages and decimal form. Convert time periods to years. Use the simple interest formula to solve for the missing quantity. Use the formula relating present and future value to solve for the missing quantity. Solve applications. HOMEWORK 20 questions due 10/12/17 5-2 HOMEWORK due 10/12/17 6-2 ----------------------------------------------------------------------------------------------------------------------------- EXAM 15 questions due 10/12/17 Test: 4-3 MyMathLab Exam: Chapters 3 and 4 EXAM 15? due 10/12/17 test Test 6-3 MyMathLab Exam: Chapter

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Introduction

Converting between percentages and decimal form, translating time periods to years, and applying formulas such as simple interest and the relationship between present and future values are fundamental skills in financial mathematics. These skills enable learners to solve a variety of practical problems related to finance, investment, and loan calculations. This paper provides a comprehensive overview of these concepts, illustrating their applications through examples and discussing relevant methods to solve related problems efficiently.

Converting Between Percentages and Decimal Form

Understanding the conversion between percentages and decimals is essential for accurate financial calculations. Percentages represent parts per hundred, whereas decimals express the same part in a decimal number. To convert a percentage to a decimal, divide the percentage by 100. For instance, 25% becomes 0.25 (25 ÷ 100 = 0.25). Conversely, to convert a decimal to a percentage, multiply by 100. For example, 0.75 becomes 75% (0.75 × 100 = 75%). These conversions are frequently used in interest rate calculations, financial analysis, and statistical data interpretation.

Converting Time Periods to Years

Time periods may be given in various units such as months, days, or years. Converting these to years standardizes the analysis. The conversion depends on the unit:

  • Months to years: divide the number of months by 12 (e.g., 18 months = 18 ÷ 12 = 1.5 years).
  • Days to years: divide the number of days by 365 or 366 for leap years. For example, 730 days ≈ 730 ÷ 365 = 2 years.
  • Weeks to years: divide by 52 (weeks per year).

These conversions facilitate the application of annual interest formulas and comparative analysis across different time frames.

Using the Simple Interest Formula

The simple interest formula is expressed as:

I = P × r × t

where:

  • I = interest earned or paid
  • P = principal amount
  • r = annual interest rate (decimal form)
  • t = time in years
  • To solve for a missing quantity, rearrange the formula accordingly. For example, to find the interest rate:

  • r = I / (P × t)

  • Similarly, to find the time:

  • t = I / (P × r)

  • This formula provides a straightforward method for calculating interest over specified time periods, crucial in loan amortization and investment scenarios.
  • Relating Present and Future Value
  • The relationship between present value (PV) and future value (FV) with simple interest is:

  • FV = PV × (1 + r × t)

  • This formula helps determine the future worth of an investment or loan, based on the present value, interest rate, and time period. Rearranging to find PV:

  • PV = FV / (1 + r × t)

  • and to find FV:

  • FV = PV × (1 + r × t)

  • Understanding this relationship is vital in financial planning, investment analysis, and savings calculations, especially when interest is not compounded.
  • Application of Concepts through Problem-Solving
  • Applying these formulas in practical problems involves careful unit conversions and algebraic manipulation. For instance, calculating the interest accrued over 18 months at a 5% annual rate involves converting months into years and applying the simple interest formula. Similarly, determining the present value of a future sum requires rearrangement of the FV and PV relationship. Practice with diverse examples enhances comprehension and proficiency.
  • Conclusion
  • Mastering conversions between percentages and decimals, time period transformations to years, and formulas for simple interest and present-future value relationships are fundamental competencies in financial mathematics. These skills support effective decision-making in loans, investments, and financial management. Regular practice and application to real-world problems reinforce understanding and ensure accuracy in calculations.
  • References
  1. Brigham, E. F., & Ehrhardt, M. C. (2016). Financial Management: Theory & Practice. Cengage Learning.
  2. Damodaran, A. (2012). Investment Valuation: Tools and Techniques for Determining the Value of Any Asset. Wiley Finance.
  3. Eggertsson, G. B. (2012). Great Inflation and Its Aftermath: The Past and Future of American Inflation. Columbia University Press.
  4. Khan, M. Y., & Jain, P. K. (2014). Financial Management (8th ed.). McGraw-Hill Education.
  5. Higgins, R. C. (2012). Analysis for Financial Management. McGraw-Hill Education.
  6. Ross, S. A., Westerfield, R. W., & Jaffe, J. (2013). Corporate Finance. McGraw-Hill Education.
  7. Investopedia. (2020). Simple Interest Definition. Retrieved from https://www.investopedia.com/terms/s/simpleinterest.asp
  8. MyMathLab. (2017). Online Resources for Financial Mathematics Practice. Pearson Education.
  9. U.S. Securities and Exchange Commission. (2021). Understanding Compound Interest. SEC.gov.
  10. Van Horne, J. C., & Wachowicz, J. M. (2008). Principles of Financial Management. Pearson Education.

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