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Economics & Personal Finance
Compound Interest
Compound Interest
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Compound interest is the process of earning interest on both the original amount of money and the interest that has already been added. It matters because small differences in interest rate, time, and compounding frequency can create large differences in final value. This is why saving early can be more powerful than saving a larger amount later. Compound interest helps explain growth in savings accounts, investments, loans, and debt.
Key Facts
- Compound interest formula: A = P(1 + r/n)^(nt)
- A is the final amount, P is the principal, r is the annual interest rate as a decimal, n is the number of compounding periods per year, and t is time in years.
- For annual compounding, the formula becomes A = P(1 + r)^t.
- Interest earned is I = A - P.
- More frequent compounding increases the final amount when P, r, and t stay the same.
- Continuous compounding uses A = Pe^(rt).
Vocabulary
- Principal
- The principal is the original amount of money invested, saved, or borrowed.
- Interest
- Interest is the extra money earned on savings or paid on a loan.
- Compound interest
- Compound interest is interest calculated on both the principal and previously earned interest.
- Interest rate
- The interest rate is the percent of the principal earned or charged over a certain time period.
- Compounding period
- A compounding period is how often interest is calculated and added to the balance.
Common Mistakes to Avoid
- Using the percent instead of the decimal form is wrong because 5% must be written as 0.05 in the formula, not 5.
- Forgetting to include compounding frequency is wrong because monthly, quarterly, and annual compounding give different final amounts.
- Multiplying simple interest by time for every problem is wrong because compound interest grows on interest already earned.
- Rounding too early is wrong because small rounding errors can grow over many compounding periods and change the final answer.
Practice Questions
- 1 A student deposits $800 in an account earning 6% annual interest compounded yearly. How much money will be in the account after 5 years?
- 2 A bank account starts with $2,000 and earns 4.8% annual interest compounded monthly. What is the balance after 3 years?
- 3 Two people each invest $1,000 at the same annual interest rate. One starts at age 20 and the other starts at age 30. Explain why the earlier investor can end with much more money even if neither adds more money.