A compound interest savings project shows how money can grow when interest is added to an account and then earns more interest over time. This matters because even small deposits can become much larger if they are left to grow for many years. Students can compare simple interest and compound interest to see why time, rate, and compounding frequency are powerful factors.
A visual savings jar, money tree, or growth chart helps turn an abstract formula into something easy to understand.
Key Facts
- Compound interest formula with annual compounding: A = P(1 + r)^n
- Compound interest formula with multiple compounds per year: A = P(1 + r/n)^(nt)
- Simple interest formula: A = P(1 + rt)
- Interest earned = A - P
- For compound interest, longer time usually creates faster growth because interest earns interest.
- Use r as a decimal, so 6% becomes 0.06 and 3.5% becomes 0.035.
Vocabulary
- Principal
- The starting amount of money saved or invested.
- Interest
- The extra money earned for keeping funds in a savings account or investment.
- Compound interest
- Interest calculated on both the original principal and the interest already earned.
- Simple interest
- Interest calculated only on the original principal.
- Compounding frequency
- How often interest is added to the account, such as yearly, monthly, or daily.
Common Mistakes to Avoid
- Using 5 instead of 0.05 for a 5% rate is wrong because formulas require the interest rate as a decimal.
- Mixing up n and t is wrong because n is the number of compounding periods per year, while t is the number of years.
- Assuming simple and compound interest grow the same way is wrong because compound interest adds interest to previous interest.
- Rounding too early is wrong because small rounding differences can become larger over long time periods.
Practice Questions
- 1 A student deposits $500 at 4% annual interest compounded once per year. How much money will be in the account after 10 years using A = P(1 + r)^n?
- 2 Compare simple and compound interest for $1,000 at 5% for 20 years. Find the final amount for simple interest using A = P(1 + rt), then find the final amount for annual compound interest using A = P(1 + r)^n.
- 3 A class project compares savings over 5, 10, 20, and 40 years. Explain why the gap between simple interest and compound interest becomes much larger after 40 years than after 5 years.