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Compound Interest

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Compound Interest

Study Guide

Key Definition

Compound interest means that you earn interest on your current balance, which includes the original principal plus all previously earned interest. This causes your investment to grow at an increasing rate.

Important Notes

Compound interest increases the amount of money you earn each year.
The calculation for each year uses the total amount from the previous year as the base figure.
This means that your increases are bigger every year.
Round monetary values to two decimal places (nearest cent).

Mathematical Notation

$P$ represents the principal amount

$r$ is the annual interest rate (as a decimal)

$t$ is the number of years the money is invested

$A$ is the amount of money accumulated after t years, including interest

$n$ is the number of times interest is compounded per year

Express interest rates as decimals (e.g., 0.05), not percents, in formulas

Why It Works

Compound interest works because the interest you earn each year is added to your principal, so that the balance doesn't merely grow, it grows at an increasing rate - it is exponential. This is the result of ‘compounding’, which is the process of earning interest on interest.

Remember

The formula for calculating compound interest is $A = P(1 + \frac{r}{n})^{nt}$ where n is the number of times that interest is compounded per unit t.

Quick Reference

Compound Interest Formula:$A = P(1 + \frac{r}{n})^{nt}$

Understanding Compound Interest

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Video explanation of this concept

Beginner

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Beginner Explanation

In compound interest, interest is added to the principal at specific intervals so that future interest is earned on past interest as well. The formula $A = P(1 + r/n)^{nt}$ shows this accumulation, where each compounding period adds interest to the total balance.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

If you invest $100 with a yearly interest rate of 6%, how much will you have after one year?

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

You're a teenager who has just received $500 for your birthday. You decide to invest it in a savings account with a yearly interest rate of 5%. How much will you have after three years?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

How does the amount of money you earn change each year with compound interest?

Challenge Quiz

Single Choice Quiz

Advanced

If you invest $1000 in a savings account with a yearly interest rate of 8%, how much will you have after five years?

Recap

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Review key concepts and takeaways