Money Grows Money: Exploring Compound Interest

Materials Needed

• Calculator or spreadsheet tool
• Notebook or math journal
• Pencil or digital writing tool
• Printed or digital reading passage
• Practice exercise sheet
• Optional: play money, index cards, and a jar labeled “Investment”

Lesson Overview

Grade/Age: 14-year-old homeschool learner

Standard: MA.912.FL.3.1 — Explore compound interest.

Length: Three 40-minute lessons

Big Idea: Money can grow faster when interest is added to an account and then earns additional interest.

Learning Objectives

By the end of the three lessons, the learner will be able to:

• Define compound interest, annual compounding, semiannual compounding, quarterly compounding, daily compounding, and crediting.
• Identify the principal, interest rate, compounding frequency, and time in a compound-interest problem.
• Use the formula A = P(1 + r/n)^nt to calculate the future value of an account.
• Compare how different compounding schedules affect the amount of money earned.
• Explain why time, interest rate, and compounding frequency matter in saving and investing.
• Apply compound interest to a realistic savings or investment decision.

Success Criteria

I can successfully complete the lesson when I can:

• Explain the key vocabulary in my own words.
• Correctly label P, r, n, t, and A in a problem.
• Use the compound-interest formula accurately.
• Round money answers to the nearest cent.
• Explain how the compounding schedule changes the final amount.
• Support a financial choice with calculations and evidence.

Important Formula and Vocabulary

Compound-interest formula:

A = P(1 + r/n)^nt

• A = final amount in the account
• P = principal, or starting amount
• r = annual interest rate written as a decimal
• n = number of times interest is compounded each year
• t = time in years

Use the following values for n:

Compounding Schedule	Meaning	Value of n
Annual	Once each year	1
Semiannual	Twice each year	2
Quarterly	Four times each year	4
Daily	Every day, usually using 365 days per year	365

Day 1: The Power of Compounding

Time: 40 minutes

Introduction: Hook and Objectives — 5 minutes

Ask:

If you put $100 in a savings account and earned interest, would you rather receive interest only on your original $100 or on your original money plus the interest you already earned? Why?

Explain that compound interest allows money to earn “interest on interest.” Share the objectives for the three-day lesson:

• Learn the vocabulary of compound interest.
• Understand how often interest is added to an account.
• Calculate and compare account balances.

I Do: Teacher or Instructor Modeling — 10 minutes

Use a simple example before introducing the full formula.

Suppose Maya deposits $100 and earns 10% interest compounded annually.

• After Year 1: $100 + 10% of $100 = $110
• After Year 2: $110 + 10% of $110 = $121
• After Year 3: $121 + 10% of $121 = $133.10

Point out that Maya earned $10 during the first year but $11 during the second year because the account had grown.

Introduce the formula:

A = P(1 + r/n)^nt

Model this example:

Find the balance of $500 invested at 6% annual interest for 2 years, compounded annually.

1. Identify the values: P = 500, r = 0.06, n = 1, and t = 2.
2. Substitute: A = 500(1 + 0.06/1)¹⁽²⁾.
3. Calculate: A = 500(1.06)² = $561.80.
4. Interpret the answer: The account earns $61.80 in interest.

We Do: Guided Discussion and Mini-Practice — 15 minutes

Read the following passage aloud together. Pause to underline key terms and discuss examples.

Reading Passage: How Compound Interest Works

Compound interest is interest earned on both the original amount of money and the interest that has already been added. The original amount deposited or invested is called the principal. For example, if you deposit $200, the principal is $200. If the account earns interest, the balance grows. Later interest may be calculated using the larger balance, allowing the money to grow more quickly.

Interest is added to an account according to a schedule. This process is called crediting. Crediting means adding earned interest to an account balance. The schedule tells you how often the interest is credited, or added, to the account.

With annual compounding, interest is credited once per year. With semiannual compounding, interest is credited twice per year, or every six months. Each six-month period uses one-half of the annual interest rate. With quarterly compounding, interest is credited four times per year, or every three months. Each quarter uses one-fourth of the annual interest rate.

With daily compounding, interest is credited each day. Financial institutions often use 365 days in a year for daily calculations. Because interest is added more frequently, daily compounding may produce a slightly larger balance than annual, semiannual, or quarterly compounding when the rate and starting amount are the same. However, the difference may be small, especially for short periods or small deposits.

The compound-interest formula is A = P(1 + r/n)^nt. In this formula, A is the final amount, P is the principal, r is the annual interest rate written as a decimal, n is the number of times interest is credited each year, and t is the number of years. The formula helps savers compare accounts and make informed decisions.

Reading-Passage Questions

1. What is compound interest?
2. What is the principal in a savings account?
3. What does crediting mean?
4. How many times per year is interest credited with annual compounding?
5. How many times per year is interest credited with semiannual compounding?
6. How many times per year is interest credited with quarterly compounding?
7. What does daily compounding mean?
8. Why can more frequent compounding lead to a slightly larger balance?
9. In the formula, what does n represent?
10. Why must an annual percentage rate be written as a decimal before using the formula?

You Do: Vocabulary Challenge — 7 minutes

Complete the following activity independently. Match each term to its description.

1. Compound interest
2. Annual compounding
3. Semiannual compounding
4. Quarterly compounding
5. Daily compounding
6. Crediting

Descriptions:

1. Interest is added four times per year.
2. Adding earned interest to an account.
3. Interest is added once per year.
4. Interest is earned on the original money and previously earned interest.
5. Interest is added every day.
6. Interest is added twice per year.

Closure and Quick Check — 3 minutes

Ask the learner to complete these sentences:

• “The most important difference between simple and compound interest is…”
• “Crediting means…”
• “The value of n for quarterly compounding is…”

Formative assessment: Listen for accurate definitions and check the vocabulary challenge.

Day 2: Calculating Compound Interest

Time: 40 minutes

Introduction and Review — 5 minutes

Play “Name That Schedule.” State a clue, and have the learner identify the compounding schedule:

• Interest is added every three months. Quarterly
• Interest is added two times each year. Semiannual
• Interest is added each day. Daily
• Interest is added once each year. Annual

I Do: Step-by-Step Formula Modeling — 10 minutes

Model a semiannual example.

How much will $800 grow to in 3 years at 4% interest compounded semiannually?

1. Identify the values: P = 800, r = 0.04, n = 2, t = 3.
2. Substitute into the formula: A = 800(1 + 0.04/2)²⁽³⁾.
3. Simplify: A = 800(1.02)⁶.
4. Calculate: A ≈ $900.95.
5. Find the interest earned: $900.95 − $800 = $100.95.

Emphasize that the rate is divided by n, while the number of compounding periods is multiplied by n.

We Do: Guided Comparison — 12 minutes

Work together to compare a $1,000 deposit earning 5% for 2 years.

Schedule	n	Set-Up
Annual	1	1000(1 + 0.05/1)1(2)
Semiannual	2	1000(1 + 0.05/2)2(2)
Quarterly	4	1000(1 + 0.05/4)4(2)
Daily	365	1000(1 + 0.05/365)365(2)

Use a calculator or spreadsheet to complete the comparison. Discuss:

• Which account has the largest final amount?
• Is the difference between annual and daily compounding large or small?
• Would the difference become more important over 20 or 30 years?

You Do: Practice Exercises 1–5 — 10 minutes

Show your work. Round final money answers to the nearest cent.

1. Find the final amount of $600 invested at 3% for 4 years, compounded annually.
2. Find the final amount of $750 invested at 4% for 5 years, compounded semiannually.
3. Find the final amount of $1,200 invested at 5% for 3 years, compounded quarterly.
4. Find the final amount of $900 invested at 6% for 2 years, compounded daily. Use 365 days per year.
5. A student deposits $400 into an account earning 5% compounded annually for 6 years. How much interest is earned?

Closure and Reflection — 3 minutes

Have the learner explain the following without looking at notes:

Why is 0.05 used instead of 5 in a problem involving a 5% interest rate?

Formative assessment: Check that the learner identifies all four variables correctly and uses the correct value for n.

Day 3: Applying Compound Interest to Real Life

Time: 40 minutes

Introduction: Financial Mission — 5 minutes

Present this scenario:

You receive $1,000 as a gift. You can place it in one of several accounts. Your goal is to have the most money after five years, but you also want to understand how the account works. How will you decide?

Explain that today the learner will use calculations and reasoning to make a financial recommendation.

I Do: Model a Financial Comparison — 8 minutes

Compare two accounts for $1,000 invested for 5 years:

• Account A: 4.5% compounded annually
• Account B: 4.4% compounded daily

Model the process:

1. Write the formula for each account.
2. Convert each percentage to a decimal.
3. Use the correct value of n.
4. Calculate and round to the nearest cent.
5. Compare the final amounts, not just the interest rates.

Discuss the idea that a higher stated rate does not always tell the entire story. Compounding frequency also matters.

We Do: Account Comparison — 10 minutes

Work together on the following problem:

An account contains $2,000 and earns 3.5% interest for 4 years. Calculate the final amount when interest is compounded annually, semiannually, quarterly, and daily.

Create a table with these headings:

Schedule	n	Final Amount	Interest Earned
Annual	1
Semiannual	2
Quarterly	4
Daily	365

Discuss which option would be best if all other account rules were the same.

You Do: Practice Exercises 6–10 — 10 minutes

6. Find the final amount of $1,500 invested at 4.2% for 7 years, compounded quarterly.
7. Find the final amount of $2,500 invested at 3.8% for 10 years, compounded semiannually.
8. Two accounts each start with $1,000 and last for 8 years. Account A earns 4% compounded annually. Account B earns 4% compounded daily. Which account has the greater final amount, and by approximately how much?
9. You want $2,000 in 5 years. You can invest $1,600 today at 4.5% compounded annually. Will you reach your goal? Show your calculation.
10. A savings account has $3,000, earns 5.5% interest, and compounds quarterly for 6 years. Calculate the final amount and total interest earned. Then write one sentence explaining what “crediting” means in this situation.

Summative Assessment: Choose Your Investment Project — 5 minutes

Choose one of the following options:

• Option A: Savings Challenge — Compare two accounts for saving money toward a purchase.
• Option B: Future Goal — Calculate how $500 could grow for college, a car, travel, or another goal.
• Option C: Spreadsheet Investigation — Create a table comparing annual, semiannual, quarterly, and daily compounding.

Your project must include:

1. A starting amount.
2. An annual interest rate.
3. A time period of at least 3 years.
4. At least two compounding schedules.
5. The compound-interest formula and substitutions.
6. Final amounts rounded to the nearest cent.
7. A written recommendation explaining which option is best and why.

Ten Practice Exercises: Answer Key

1. $675.30
2. $915.79
3. $1,393.96
4. $1,014.49
5. $537.23 total; $137.23 interest
6. $2,009.22
7. $3,635.54
8. Account B; approximately $4.44 more
9. $1,994.19; No, the goal is short by approximately $5.81
10. $4,163.69 total; $1,163.69 interest

Conclusion and Recap

Ask the learner to answer these questions orally or in writing:

1. What is compound interest?
2. What does the compounding schedule tell you?
3. How are annual, semiannual, quarterly, and daily compounding different?
4. What does crediting mean?
5. How can compound interest help someone reach a financial goal?

End with this key takeaway:

Compound interest allows money to earn interest on previously earned interest. The amount of growth depends on the starting amount, interest rate, time, and how often interest is credited.

Differentiation and Adaptations

Support for Learners Who Need More Practice

• Provide a formula card listing P, r, n, and t.
• Allow the learner to use a calculator or spreadsheet.
• Begin with annual compounding before moving to more frequent schedules.
• Use color coding: principal in blue, rate in green, compounding frequency in purple, and time in orange.
• Complete the first few problems together before independent practice.

Extension for Advanced Learners

• Investigate continuous compounding using the formula A = Pe^rt.
• Compare compound interest with simple interest.
• Explore how regular monthly deposits change the final amount.
• Research the difference between an interest rate and an annual percentage yield, or APY.
• Determine how long it takes an investment to double under different interest rates.

Flexible Delivery Options

• Homeschool: Use a household savings goal, such as a bicycle, computer, or trip.
• Classroom: Have pairs compare different account offers and present recommendations.
• Training or digital learning: Use an online calculator or spreadsheet and submit the project electronically.
• Hands-on option: Represent each compounding period with play money or index cards to show how interest is repeatedly added to the balance.