Personal Finance Unit 4: Saving and Investing | Notes and practice

Notes

Simple interest: $I = Prt$ (principal times yearly rate as a decimal times years). Compound interest: $A = P(1 + r)^t$, which earns interest on interest.
Rule of 72: years to double $\displaystyle \approx \frac{72}{\text{rate in percent}}$. At 9%, about 8 years.

A stock is ownership in a company; a bond is a loan that pays interest. Stocks tend to have higher risk and higher possible return.
A mutual fund pools money into many investments. An index fund tracks a market index and usually has low fees. Fee per year $=$ balance $\times$ expense ratio.

Higher possible return usually means higher risk. Diversification spreads risk. Longer time horizons can handle more risk.

401(k): employer plan, often with a match. IRA: account you open yourself. Traditional accounts are usually taxed at withdrawal; Roth accounts are taxed before deposit. Early withdrawals often bring taxes and penalties.

Each topic has its own short notes and practice.

How much simple interest does $1,500 earn at 4% per year for 3 years?

$1,000 earns 10% compounded yearly. What is it worth after 2 years?

About how long does it take money to double at a 4% annual growth rate?

Which investment is a loan to a company or government that pays interest?

Which strategy most reduces the risk from any single investment losing value?

Maria earns $60,000 and contributes 5% to a 401(k). Her employer matches 50% of her contribution. How much does the employer add?

Write your answer first, then open the scoring guide.

Free-response question

Jordan invests $2,000 at 5% interest per year. Use made-up numbers and ignore fees and taxes.

(a) Find the simple interest after 3 years.

Show the answer and scoring guide

$I = 2000 \times 0.05 \times 3 = 300$, so $300.

Check off the points you earned:

(b) If the account instead compounds yearly, find the value after 2 years and the interest earned.

Show the answer and scoring guide

Year 1: $2000 \times 1.05 = 2100$. Year 2: $2100 \times 1.05 = 2205$. Interest earned is $205.

Check off the points you earned:

(c) Use the Rule of 72 to estimate how long it takes for Jordan's money to double at 6% and explain why starting early helps.

Show the answer and scoring guide

$\displaystyle \frac{72}{6} = 12$ years. Starting early gives money more time to double, and compounding means earlier growth also earns growth.

Check off the points you earned: