Homeschool · Diploma track · Grades 11-12
Financial Algebra: free lessons and course outline
A full year of Financial Algebra, built to be the student's whole course in personal finance rather than a supplement to one. The algebra in this subject is mostly percentages and exponential growth, and it is not the hard part. The hard part is the setup: which number is the principal, whether a rate is annual or monthly, which percent is taken of what, and what the question is really asking for. Eleven units take the year from a first paycheck through income tax, budgeting and banking, simple and compound interest, saving over decades, credit cards and loans, cars and housing, insurance, and investing, and end by assembling a complete plan. Every number in every solution is named before it is used, every solution is worked line by line, and every answer is checked against what a sensible person would expect.
Financial Algebra is the rare math course whose problems describe decisions a student will actually make, and most of those decisions are made once, early, with little practice. The eleven units follow the order in which money arrives and leaves. Unit 1 follows a paycheck from the hours worked to the amount deposited, Unit 2 explains the income tax taken from it, and Unit 3 turns what remains into a budget and a bank account. Units 4 and 5 are the mathematical heart of the course: simple and compound interest, then regular saving and the time value of money, where a single idea (money grows in steps, and each step grows on the last) explains savings, loans and retirement at once. Units 6 and 7 run the same idea in reverse for credit cards and loans. Unit 8 prices the two largest purchases most people make, a car and a home. Unit 9 measures risk and what insurance costs, Unit 10 turns to investing, and Unit 11 gathers everything into net worth, cash flow and a complete plan. Every lesson opens with the method, names the specific error that costs the marks, works an example in full, and then gives ten practice problems with complete solutions. Tax rates and brackets used here are teaching figures, stated as such in each problem, and are not current tax advice.
- U1Unit 1: Earning and Paychecks7 lessons
- U2Unit 2: Income Taxes7 lessons
- U3Unit 3: Budgeting and Banking6 lessons
- U4Unit 4: Simple and Compound Interest7 lessons
- U5Unit 5: Saving and the Time Value of Money7 lessons
- U6Unit 6: Credit Cards7 lessons
- U7Unit 7: Loans7 lessons
- U8Unit 8: Cars and Housing8 lessons
- U9Unit 9: Insurance and Risk6 lessons
- U10Unit 10: Investing7 lessons
- U11Unit 11: Planning as a Whole6 lessons
Every lesson, unit by unit
U1 is free to read below. The other units open with a free month or a paid plan.
U1 Unit 1: Earning and PaychecksFREE
U2 Unit 2: Income Taxes
- 2.1 Marginal tax brackets
- 2.2 Effective rate against marginal rate
- 2.3 Deductions and credits
- 2.4 Filing a simple return
- 2.5 Sales, property and other taxes
- 2.6 Withholding, refunds and estimated payments
- 2.7 Flat, progressive and regressive taxes
U3 Unit 3: Budgeting and Banking
- 3.1 Building a budget from net pay
- 3.2 Fixed, variable and irregular expenses
- 3.3 Checking accounts and reconciliation
- 3.4 Savings accounts and APY
- 3.5 Debit cards, overdrafts and the cost of banking
- 3.6 Emergency funds and saving goals
U4 Unit 4: Simple and Compound Interest
- 4.1 Simple interest
- 4.2 Compound interest
- 4.3 Compounding frequency and continuous compounding
- 4.4 APR against APY
- 4.5 Time to double and the rule of 72
- 4.6 Inflation and purchasing power
- 4.7 Comparing accounts
U5 Unit 5: Saving and the Time Value of Money
- 5.1 Future value of regular deposits
- 5.2 Present value
- 5.3 Saving toward a goal
- 5.4 Why starting early wins
- 5.5 Retirement accounts and the employer match
- 5.6 Traditional against Roth accounts
- 5.7 Withdrawals and how long savings last
U6 Unit 6: Credit Cards
- 6.1 How credit card interest is charged
- 6.2 Minimum payments and payoff time
- 6.3 The average daily balance
- 6.4 Fees, the grace period and cash advances
- 6.5 Credit reports and scores
- 6.6 What a credit score costs in dollars
- 6.7 Paying down several debts: avalanche and snowball
U7 Unit 7: Loans
- 7.1 Installment loans and the payment formula
- 7.2 Amortization tables
- 7.3 Total interest and the term
- 7.4 Extra payments
- 7.5 Student loans
- 7.6 Payday loans and annualized cost
- 7.7 Comparing loan offers
U8 Unit 8: Cars and Housing
- 8.1 The full cost of buying a car
- 8.2 Depreciation
- 8.3 Financing against leasing
- 8.4 Renting
- 8.5 The mortgage payment
- 8.6 Closing costs and the full monthly cost of owning
- 8.7 Affordability ratios
- 8.8 Refinancing and home equity
U9 Unit 9: Insurance and Risk
- 9.1 Premiums, deductibles and out-of-pocket maximums
- 9.2 Expected value and the price of risk
- 9.3 Auto and homeowners insurance and coinsurance
- 9.4 What health coverage costs in a year
- 9.5 Life and disability insurance
- 9.6 Choosing a deductible: the break-even analysis
U10 Unit 10: Investing
- 10.1 Stocks and the return on an investment
- 10.2 Bonds
- 10.3 Funds and the cost of fees
- 10.4 Risk and diversification
- 10.5 Average return against compound return
- 10.6 Dividend yield and price to earnings
- 10.7 Recognizing investment fraud
U11 Unit 11: Planning as a Whole
- 11.1 Net worth and financial statements
- 11.2 Cash flow and the savings rate
- 11.3 Unit pricing, discounts and markup
- 11.4 Cost of living and relocation
- 11.5 Buy, borrow or save: comparing the true cost
- 11.6 Building a complete financial plan
Keep going in the full Financial Algebra course
All of U1 (Unit 1: Earning and Paychecks) is free to everyone, with no account. The course has 75 lessons, each with worked examples and practice problems that come with full solutions. A free account can also start a free month of the whole course, with no card.
Open this lesson in the courseSee the whole course