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Financial Literacy
Grade 7-12
Simple vs Compound Interest Compared Cheat Sheet
A printable reference covering simple interest, compound interest, compounding frequency, growth estimates, and borrowing or saving decisions for grades 7-12.
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Simple and compound interest are two ways money can grow when saved or cost more when borrowed. This cheat sheet helps students compare how each method works, when each formula is used, and why compounding can make a big difference over time. It is useful for understanding savings accounts, loans, credit cards, investments, and financial choices.
Key Facts
- Simple interest is calculated with I = P × r × t, where P is principal, r is annual interest rate as a decimal, and t is time in years.
- The total amount with simple interest is A = P + I or A = P(1 + rt).
- Compound interest is calculated with A = P(1 + r/n)^(nt), where n is the number of compounding periods per year.
- For annual compounding, the compound interest formula becomes A = P(1 + r)^t.
- Interest earned from compounding increases over time because interest is added to both the original principal and earlier interest.
- A higher compounding frequency, such as monthly instead of yearly, usually gives a slightly larger final amount when the rate and time are the same.
- The Rule of 72 estimates doubling time with years to double ≈ 72 ÷ annual interest rate percent.
- When comparing financial options, use the same principal, rate format, time unit, and compounding frequency before deciding which option costs or earns more.
Vocabulary
- Principal
- The original amount of money saved, invested, or borrowed before interest is added.
- Interest
- The extra money earned on savings or paid as the cost of borrowing money.
- Simple Interest
- Interest calculated only on the original principal for the entire time period.
- Compound Interest
- Interest calculated on the principal plus any interest that has already been added.
- Compounding Frequency
- How often interest is added to the account balance, such as yearly, quarterly, monthly, or daily.
- Annual Percentage Rate
- The yearly interest rate written as a percent, usually used to compare loans or savings products.
Common Mistakes to Avoid
- Using the percent instead of the decimal rate, such as using 6 instead of 0.06, gives an answer that is 100 times too large.
- Forgetting to match time units with the rate is wrong because an annual rate must use time measured in years unless it is converted.
- Using the simple interest formula for a compound interest problem misses interest earned on earlier interest and usually underestimates growth.
- Ignoring compounding frequency is wrong because monthly, quarterly, and yearly compounding can produce different final balances.
- Comparing loans or accounts only by the interest rate can be misleading because fees, time length, and compounding rules also affect the total cost or earnings.
Practice Questions
- 1 A student deposits $500 at 4% simple interest for 3 years. How much interest is earned, and what is the final amount?
- 2 A savings account has $800 at 5% interest compounded annually for 2 years. What is the final amount?
- 3 Which earns more after 4 years: 1,000 at 6% compounded annually? Find both amounts.
- 4 Explain why compound interest is helpful for long-term saving but can be risky for unpaid credit card debt.