4: Financial Mathematics
- Page ID
- 181922
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)- 4.1: Understanding Percent
- This section focuses on the U.S. federal budget with an emphasis on the National Park Service and financial literacy through understanding percentages. It offers methods for converting between percent, decimal, and fractional forms, along with practical examples and exercises for calculating totals and percentages in real-life contexts.
- 4.2: Discounts, Markups, and Sales Tax
- This section explains the calculation of discounts, markups, and sales tax in retail transactions. It covers formulas for determining sale prices, original prices, and the impact of multiple discounts. The text illustrates how to calculate retail prices based on markup percentages and tax calculations, providing examples and practice exercises. Additionally, it includes information about sales tax rates, a historical context for West Virginia's taxes, and prompts for further exploration.
- 4.3: Simple and Compound Interest
- This section covers simple interest in loans and investments, explaining essential concepts like borrowers, lenders, and the formula for calculation. It provides examples for both integer and non-integer loan terms, along with practice exercises for computing simple interest and total repayments. Additionally, it introduces certificates of deposit (CDs) as a safe investment option that accrues consistent interest.
- 4.4: Methods of Savings (Annuities, Stock, and Bonds)
- This section covers the essentials of savings and investment strategies, detailing various savings accounts, investment types (stocks, bonds, mutual funds), their benefits, and risks. It explains the calculation of returns on investment (ROI), future values of annuities, and budgeting strategies. Historical context is provided regarding the FDIC's role after the 1929 crash, along with insights on retirement accounts like IRAs and 401(k)s, including contribution matches from employers.
- 4.5: Basics of Loans (Mortgage, Cars, and Credit Cards)
- This section covers various financial topics, primarily focusing on loans, credit usage, and associated calculations. It outlines the significance of credit scores, interest rates, and amortization in loan management, illustrating concepts with examples of mortgages, car loans, and credit cards. The content contrasts renting versus buying homes, details credit card types and management, and provides insights into financing car purchases and insurance essentials.
- 4.6: Income Tax and FICA Taxes
- This section covers the components and calculations of federal income tax in the U.S., including gross income, adjusted gross income (AGI), taxable income, and the differences between tax deductions and credits. It explains FICA taxes, the progressive income tax system, and provides examples across various scenarios, including families and individuals, detailing how to determine taxable income, owed taxes, and the impact of deductions and credits.