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Personal Finance Unit 3: Saving and investing

Compound interest grows money over time, and investing balances risk and return through diversification and long-term accounts.

Covers: Interest and compound growth, savings vehicles, risk and return, stocks, bonds and funds, diversification, retirement accounts

Study guide

Saving sets money aside for future goals, while investing puts money into assets that can grow. Simple interest is paid only on the original principal: I = P × r × t. Compound interest earns interest on both the principal and past interest: A = P(1 + r/n)^(nt). Starting early matters because compounding grows faster over time. The rule of 72 estimates how many years it takes money to double: 72 ÷ the annual interest rate. Inflation reduces purchasing power, so money must grow faster than inflation to gain real value. Savings options include savings accounts, high-yield savings accounts, money market accounts and certificates of deposit (CDs), which pay higher interest for locking money up for a set time.

Investments trade off risk and return: higher potential returns usually come with higher risk. Stocks are shares of ownership in a company; they can grow through price increases and dividends but can also lose value. Bonds are loans to companies or governments that pay interest; they're generally less risky than stocks. Mutual funds pool many investors' money to buy a mix of assets, and index funds and exchange-traded funds (ETFs) track a market index like the S&P 500 at low cost. Diversification, spreading money across many investments, lowers risk. Asset allocation is how you divide money among stocks, bonds and cash, often shifting toward safer investments as a goal gets closer. Fees and expense ratios reduce returns over time.

Retirement accounts offer tax advantages. A 401(k) or 403(b) is offered by employers, often with an employer match, which is free money. Traditional accounts are funded with pre-tax money and taxed when withdrawn; Roth accounts are funded with after-tax money and grow tax-free. Individual retirement accounts (IRAs) can be opened by anyone with earned income. Contribution limits are set each year by the IRS, and early withdrawals usually face penalties. Other options include 529 plans for education. Investors should be wary of scams, like Ponzi schemes and 'guaranteed' high returns.

Bond prices move opposite to interest rates. When market rates rise, older bonds that pay lower rates become less attractive, so their prices fall. When rates fall, existing bond prices rise. The expected value of an uncertain choice is each possible outcome multiplied by its probability, then added together. Two investments can carry different risks but have the same expected return.

A Ponzi scheme pays earlier investors with money from newer investors instead of from real profits. It collapses when new money stops coming in. Promises of high, steady, "guaranteed" returns are a warning sign. The more often interest compounds (daily rather than monthly or yearly), the faster savings grow at the same stated rate. The annual percentage yield (APY) includes the effect of compounding, so it is the best way to compare savings accounts.

Your real return is roughly your nominal (stated) interest rate minus the inflation rate. Earning 2% while prices rise 3% means a real return of about −1%, so your money buys less.

Key ideas

• Compound interest earns interest on past interest, so starting early matters.
• The rule of 72 estimates doubling time.
• Higher potential returns usually mean higher risk.
• Diversification lowers risk; index funds are low-cost and diversified.
• Retirement accounts offer tax benefits, and employer matches are free money.

Formulas and rules

Common mistakes

• Thinking bonds are ownership in a company; stocks are ownership, bonds are loans.
• Skipping an employer match; it's an instant return on your contribution.

Words to know

Principal

The original amount saved or borrowed.

Simple interest

Interest paid only on the principal.

Compound interest

Interest earned on principal and past interest.

Rule of 72

Estimates doubling time: 72 ÷ interest rate.

Inflation

A general rise in prices that lowers purchasing power.

Certificate of deposit (CD)

A savings product with a fixed term and rate.

Risk-return tradeoff

Higher potential returns come with higher risk.

Stock

A share of ownership in a company.

Dividend

A portion of company profit paid to shareholders.

Bond

A loan to a company or government that pays interest.

Mutual fund

A pool of investors' money buying many assets.

Index fund

A fund that tracks a market index.

ETF

An exchange-traded fund that trades like a stock.

Diversification

Spreading money across many investments.

Asset allocation

How money is divided among stocks, bonds and cash.

Expense ratio

The yearly fee a fund charges.

401(k)

An employer-sponsored retirement account.

Employer match

Employer contributions that match an employee's savings.

Roth account

Retirement account funded with after-tax money that grows tax-free.

IRA

An individual retirement account.

Sample practice questions

21 more questions like these, from level 1 to 5, are in the practice set.