Compound Interest

7.4 Compound Interest

Description

Quick Overview

This section introduces compound interest, explaining how it differs from simple interest and providing methods for its calculation.

Standard

Compound interest is discussed as the interest calculated on the principal amount and the accumulated interest from previous periods. The section provides examples illustrating how compound interest increases over time and introduces a formula to calculate it.

Detailed

In this section, we learn about compound interest, which is calculated on the initial principal and also on the accumulated interest from previous periods. This concept is vital for understanding how savings and investments grow over time. The formulas, examples, and methods to calculate compound interest are discussed, illustrating the benefits of this approach over simple interest. Compound interest leads to exponential growth, making it essential for financial education and planning. By analyzing various examples, students can grasp how compound interest accumulates faster than simple interest, and they will learn the formula: A = P(1 + r/n)^(nt), where A is the amount, P is the principal, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.

Key Concepts

  • Compound Interest: Interest calculated on the principal and on the accumulated interest of previous periods, leading to exponential growth over time.

  • Principal: The original sum of money before interest.

  • Amount Formula: A = P(1 + r/n)^(nt) provides a way to calculate the total amount including interest.

Memory Aids

🎵 Rhymes Time

  • Compounding's a magic trick, interest grows thick, every year it stacks high, watch your savings fly!

📖 Fascinating Stories

  • Once there was a farmer named Joe who planted seeds every year. The first year, he planted $100 worth; each year, he added interest. His fields flourished more each year because his returns grew faster than before.

🧠 Other Memory Gems

  • P.A.R.T. - Principal, Amount, Rate, Time help remember key components for compound interest.

🎯 Super Acronyms

C.I. - Compound Interest, a way money grows with magic over time!

Examples

  • If you invest $1,000 at an annual interest rate of 5% compounded annually, after one year, you will have $1,050. After the second year, you will have $1,102.50.

  • If you borrow $2,000 at an interest rate of 10% compounded annually for 3 years, the total amount due after 3 years will be $2,662.30.

Glossary of Terms

  • Term: Principal (P)

    Definition:

    The original sum of money invested or borrowed.

  • Term: Compound Interest (C.I.)

    Definition:

    Interest calculated on the principal and the accumulated interest from previous periods.

  • Term: Rate (r)

    Definition:

    The percentage charged or earned on the principal over a specified time.

  • Term: Amount (A)

    Definition:

    The total amount of money that includes both the principal and the interest earned.

  • Term: Time (t)

    Definition:

    The duration for which the money is invested or borrowed, typically measured in years.