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This cheat sheet covers the main formulas and decision rules students need for investing, credit, and taxes. It is designed as a quick reference for comparing savings growth, loan costs, credit choices, and paycheck deductions. Students need these tools to understand how money grows, how debt becomes expensive, and how taxes affect take-home pay.

Key Facts

  • Simple interest is I = PRT, where P is principal, R is annual interest rate as a decimal, and T is time in years.
  • Compound interest is A = P(1 + r/n)^(nt), where A is final amount, P is principal, r is annual rate, n is compounding periods per year, and t is years.
  • Investment return is ROI = (ending value - starting value + income) / starting value x 100%.
  • Loan payment cost can be compared using total repayment = monthly payment x number of payments.
  • Credit utilization is utilization = credit card balance / credit limit x 100%, and lower utilization usually helps a credit score.
  • Taxable income is taxable income = gross income - adjustments - deductions.
  • Effective tax rate is effective tax rate = total tax paid / gross income x 100%.
  • Net pay is net pay = gross pay - federal tax - state tax - payroll taxes - other deductions.

Vocabulary

Principal
Principal is the original amount of money invested, saved, or borrowed before interest is added.
Compound Interest
Compound interest is interest earned on both the original principal and previously earned interest.
APR
APR, or annual percentage rate, is the yearly cost of borrowing money, including interest and certain fees.
Credit Score
A credit score is a number that estimates how likely a borrower is to repay money on time.
Tax Deduction
A tax deduction lowers taxable income, which can reduce the amount of tax owed.
Effective Tax Rate
Effective tax rate is the percent of total income that is actually paid in taxes.

Common Mistakes to Avoid

  • Using 8 instead of 0.08 for an 8% interest rate is wrong because formulas require percent rates to be written as decimals.
  • Confusing simple interest with compound interest is wrong because compound interest grows faster by adding interest on past interest.
  • Looking only at the monthly payment is misleading because a lower payment can still cost more if the loan term is longer.
  • Assuming a tax deduction reduces tax dollar for dollar is wrong because a deduction lowers taxable income, not the tax bill directly.
  • Carrying a high credit card balance is risky because high credit utilization can lower a credit score and increase interest charges.

Practice Questions

  1. 1 You invest $800 at 6% annual interest compounded monthly for 5 years. Use A = P(1 + r/n)^(nt) to find the approximate final amount.
  2. 2 A credit card has a 2,500limitanda2,500 limit and a 900 balance. Find the credit utilization percentage.
  3. 3 A worker earns 48,000andpays48,000 and pays 6,720 in total taxes. Find the effective tax rate.
  4. 4 Explain why two loans with the same monthly payment can have very different total costs.

Understanding Investing Credit and Taxes

Compound growth has an important timing effect. Money earns a return, then later returns can be earned on the earlier returns. This makes the first years of saving especially valuable.

A student who starts with small regular deposits can sometimes build more than someone who waits and deposits larger amounts later. The rate matters, but time often matters just as much. Inflation must be considered too.

If prices rise faster than an account grows, the money may buy less over time. Investments can increase in value, pay income, fall in value, or do all of these at different times.

Higher possible returns usually come with a greater chance of losses. Spreading money across different investments reduces the harm from one company or industry doing poorly.

A credit score is not a grade for being a good person. It is a prediction tool used by lenders to estimate repayment risk. Paying every bill by its due date is usually one of the strongest signals.

Keeping card balances low compared with available limits can help because high balances may suggest financial pressure. Opening many accounts in a short period can create concern, especially when lenders check an application. Old accounts can be useful because they show a longer record, but closing an old card may reduce available credit and raise utilization.

A card should not be kept open if its fee or spending temptation creates a bigger problem. The safest habit is to charge only an amount that can be paid in full when the statement arrives.

Loan payments can feel manageable each month while the total cost is much larger than the amount borrowed. This happens because interest is charged over time. In many installment loans, early payments send more money toward interest than toward the original balance.

This pattern is called amortization. A longer loan term often lowers the monthly payment, yet it usually increases total interest. A shorter term can cost more each month while reducing the overall cost.

Students commonly see this tradeoff with car loans, student loans, and phone financing. Before accepting a loan, compare the amount financed, the annual percentage rate, the payment length, fees, and the full repayment amount. Missing payments can add fees, increase interest costs, and damage credit history.

Taxes require careful attention because a paycheck is not the same as earned income. Employers withhold estimated federal, state, and payroll taxes from each check. Payroll taxes support programs such as Social Security and Medicare.

The amount withheld is an estimate based on payroll information. At tax filing time, the final tax is calculated using yearly income, deductions, credits, and other details. A refund often means too much was withheld during the year.

It is not extra income from the government. Owing tax can mean too little was withheld or that income came from work without automatic withholding. When solving school problems, label every amount clearly.

Separate annual figures from monthly figures, convert percentages to decimals when needed, and check whether a result describes a payment, a balance, a return, or a tax rate. These labels prevent many common mistakes.