Math & numbers Ideas & discovery

How to understand compound interest

See how compounding works, for you and against you.

Compound interest includes interest on accumulated interest. Calculate one period at a time using a stated rate and compounding schedule. The example below separates this arithmetic from any promise about investment returns or the terms of a real loan.

Want new features first?

Start with three things you can do today

A starting goal

I want to understand compound interest properly, for savings, loans and investing. Show me how it works, why time matters so much, and how to run the numbers myself without a spreadsheet.

Change any word so it fits your situation. The course is built from what you type and a few setup questions.

Start today

Three things you can do before the course exists.

Useful on their own. The course is for when you want the whole skill, not just the first move.

Calculate the first two years
Original hypothetical savings example: $1,000 earns a fixed 5% annually, with interest added once each year and no deposits, withdrawals, fees or tax. Year 1 ends at $1,050. Year 2 interest is 5% of $1,050, or $52.50, giving $1,102.50.
Compare with simple interest
At simple interest of 5% on the original $1,000 only, each year adds $50. Two years would give $1,100. The extra $2.50 in the compound example is interest earned on the first year's $50. Check:0.05 x 50 =2.50.
Change assumptions before applying it
Real rates, timing, fees, contributions and loan repayments can change the result. Debt does not follow the no-payment example when repayments reduce principal. Read the actual terms and use the right period; this is an explanation, not a forecast or a recommendation to borrow or invest.

Sources: SEC Investor.gov: definition of compound interest. Practical examples are starting points, not promised results.

Best for: Math & numbers
Prerequisites: None. Bring the situation you have.
Course length: 7 to 30 lessons
Pace: Yours. One lesson at a time, as often as you like.
Format: Read it, or play the audio
Access: Available on the App Store and Google Play, with an optional early testing list

Before the course is built

Setup asks about your situation first.

Lesson 1 opens on the moment you describe, and the examples use your role. For this request, expect questions like these.

Is this mainly about savings, debt, investing, or all of them?
How comfortable are you with percentages?
Is there a decision you want to run the numbers on?

Right for now

If any of this sounds familiar, start here.

You have heard it is powerful and do not see why

The numbers in the examples seem made up.

You have a loan and do not understand the total

How did borrowing that become paying this?

You want to run the numbers

Without a spreadsheet or a calculator app.

Course arc

Where the course goes, in order.

Cadence writes the lessons for you, so the exact path follows your answers. This is the ground a course built from this sentence covers.

01 / 06

Simple versus compound

Comparing interest on the original amount with interest on the growing balance.

The curve

Following balances over equal periods under explicitly fixed assumptions.

Rate, time, contribution

Which lever matters most, and when.

Compounding against you

Debt, fees and the cost of the minimum payment.

Shortcuts

Rule of seventy two, doubling and rough estimates.

Decisions

Pay down debt or save, and how to compare.

What changes

What you will be able to do, and what you will stop believing.

You will be able to

Understand compounding

Interest on interest, and why the curve bends.

See why time matters

Starting early versus contributing more.

Understand it on debt

Credit cards, minimum payments and how balances grow.

Estimate in your head

The rule of seventy two and other shortcuts.

Ideas this course corrects

A higher rate always matters more than starting earlier

The result depends on rate, time, contributions, fees and other conditions. Compare the stated assumptions.

Every investment or loan compounds in the same way

Compounding schedules, variable returns and repayments differ. A simple illustration does not replace the actual terms.

Course questions

What to know before you start.

How to understand compound interest: what can I do today?

Calculate the first two years. Original hypothetical savings example: $1,000 earns a fixed 5% annually, with interest added once each year and no deposits, withdrawals, fees or tax. Year 1 ends at $1,050. Year 2 interest is 5% of $1,050, or $52.50, giving $1,102.50. Compare with simple interest. At simple interest of 5% on the original $1,000 only, each year adds $50. Two years would give $1,100. The extra $2.50 in the compound example is interest earned on the first year's $50. Check:0.05 x 50 =2.50. Change assumptions before applying it. Real rates, timing, fees, contributions and loan repayments can change the result. Debt does not follow the no-payment example when repayments reduce principal. Read the actual terms and use the right period; this is an explanation, not a forecast or a recommendation to borrow or invest.

Is this a fixed course?

No. Cadence builds the course when you type the sentence and answer a few setup questions, so the lessons follow your situation. This page describes what a course built from this request covers. You see the whole path before Lesson 1.

Who is this course for?

Do I need any prior experience?

No. Setup asks what you already know and where you want to use it, and the course starts from there. Bring a real situation if you have one; the examples are built around it.

How long does it take?

Most courses run 7 to 30 lessons. The course length is sized to what you asked for. You set the pace: one lesson at a time, as often as you like. Lessons can be read or played as audio.

Does this course award a certificate or degree?

No. Cadence is for practical self-learning and does not award accredited degrees or professional certification.