F. Financial Literacy · Money and Finances: Payments, Financial Plans, Budgets, Interest and Smart Spending

Simple Interest and Compound Interest

F1.4 A1About 45 minutes

Learning goals

I can calculate simple interest using I = P × r × t.
I can calculate compound interest year by year and with the formula A = P(1 + r)ⁿ.
I can compare the growth of simple and compound interest at different rates.
I can explain why compound interest grows faster over time.

Words to know

principal (P)
The amount of money first saved, invested or borrowed.

interest rate (r)
The percent paid or charged per year, written as a decimal in formulas: 5% = 0.05.

simple interest
Interest paid only on the principal. It's the same amount every year.

compound interest
Interest paid on the principal and on interest already earned, so the amount grows faster each year.

amount (A)
The total after interest: principal + interest.

compounded annually
Interest is calculated and added once a year.

Remember from Grade 7

In Grade 7 you found savings balances year by year: interest = rate × balance, then add it on. You saw that interest earns interest over time, and that higher rates and more time mean more growth (or more cost, when borrowing).

In Grade 8 you'll give these two kinds of interest their names, simple and compound, write a formula for each, and compare them carefully.

Two ways to pay interest

Imagine you lend $1 000 to a bank at 5% a year for 10 years (that's what a savings deposit really is).

With simple interest, the bank pays 5% of $1 000 every year: $50, $50, $50... After 10 years: 10 × 50 = $500 of interest.
With compound interest, each year's interest is added to the balance, and the next year's 5% is on the bigger balance. The interest grows: $50, then $52.50, then $55.13...

Simple interest formula

I = P × r × t

I = interest, P = principal, r = yearly rate as a decimal, t = time in years.
Total amount: A = P + I.

Compound interest formula (compounded once a year)

Each year the balance is multiplied by (1 + r). After n years:

A = P(1 + r)ⁿ

That's the exponent you learned in Grade 7! 1 000 × 1.05 × 1.05 × 1.05 = 1 000 × 1.05³.

All rates in this lesson are examples. Real accounts may compound monthly or even daily, but the idea is the same.

$1 000 at 5% for 3 years. Compound interest takes 5% of the new balance, so the yearly interest grows ($50, $52.50, $55.13). Simple interest stays at $50.

Worked example

Example 1: Simple interest

Find the simple interest and the total amount for $2 000 at 4% a year for 5 years.

P = 2 000, r = 0.04, t = 5.
I = 2 000 × 0.04 × 5 = 80 × 5 = $400.
A = 2 000 + 400 = $2 400.

Interest $400, total $2 400.

Year	Start balance	Interest (4%)	End balance
1	$2 000.00	$80.00	$2 080.00
2	$2 080.00	$83.20	$2 163.20
3	$2 163.20	$86.53	$2 249.73
4	$2 249.73	$89.99	$2 339.72
5	$2 339.72	$93.59	$2 433.31

$2 000 at 4% compounded annually, rounded to the cent each year.

Worked example

Example 2: Compound interest, same numbers

Find the amount for $2 000 at 4% compounded annually for 5 years. Compare with simple interest.

Year by year (see the table): each year, interest = 0.04 × start balance.
Or use the formula: A = 2 000 × 1.04⁵.
1.04⁵ = 1.2166529..., so A = 2 000 × 1.2166529 ≈ $2 433.31.
Compound interest: 2 433.31 − 2 000 = $433.31. Simple interest was $400.

Compound interest earns $33.31 more in 5 years, because each year's interest also earns interest.

$1 000 at 5% a year. Simple interest grows by the same $50 every year: $1 250, $1 500, $1 750, $2 000. Compound interest grows faster and faster: about $1 276, $1 629, $2 079, $2 653. Bars are drawn to scale.

Worked example

Example 3: The gap grows with time

$1 000 at 5% for 10 and 20 years. Compare simple and compound.

Simple, 10 years: I = 1 000 × 0.05 × 10 = 500. A = $1 500.
Compound, 10 years: 1 000 × 1.05¹⁰ = 1 000 × 1.6288946... ≈ $1 628.89.
Simple, 20 years: I = 1 000 × 0.05 × 20 = 1 000. A = $2 000.
Compound, 20 years: 1 000 × 1.05²⁰ ≈ $2 653.30.

The gap is $128.89 after 10 years but $653.30 after 20 years. With compound interest, time makes a huge difference.

Worked example

Example 4: Compound interest on a debt

Someone owes $1 000 at 20% a year and makes no payments for 3 years (a simplified example). Compare simple and compound interest.

Simple: I = 1 000 × 0.20 × 3 = 600. A = $1 600.
Compound: A = 1 000 × 1.20³ = 1 000 × 1.728 = $1 728.

With compound interest the debt is $1 728, which is $128 more than with simple interest. Compounding works against you when you borrow.

Watch out!

Change the percent to a decimal: 4% = 0.04, 4.5% = 0.045, not 0.4.
In the compound formula, add 1 to the rate first: 1 + 0.04 = 1.04. Multiplying by 1.04 keeps the old balance and adds 4%.
Use a calculator's exponent key (often written xʸ, yˣ or ^) for 1.04⁵. Round money to the cent at the end. Year-by-year tables rounded each year may differ by a cent.

Estimate first

Before calculating, estimate. Simple interest at 5% for 10 years is 50%, so $1 000 grows to $1 500. Compound must be a bit more than that. If your calculator says $16 288.95, you know a decimal slipped.

Just for fun

Why is compound interest so good at conversations?

It finds everything interesting, even its own interest.

Hands-on activity

Bean-counter interest

You need: about 150 dried beans (or buttons, or paper clips), two bowls, and paper. (Keep small objects away from young children.)

Put 20 beans in each bowl. Each bean stands for $10. That's $200 in each "account".
Bowl A gets simple interest of 25% per round: always add 25% of the original 20 beans = 5 beans.
Bowl B gets compound interest of 25% per round: add 25% of what's in the bowl now, rounded to the nearest bean. Round 1: 25% of 20 = 5 → 25. Round 2: 25% of 25 = 6.25 → add 6 → 31.
Do 5 rounds and record both bowls in a table. Keep a column for the exact compound value too (20 × 1.25ⁿ).
Which bowl pulls ahead? When did the difference become clear?

What to look for: Bowl A: 25, 30, 35, 40, 45. Bowl B (rounding beans each round): 25, 31, 39, 49, 61. Exact compound: 25, 31.25, 39.06, 48.83, 61.04. The compound bowl grows faster every round. (25% is a big rate, chosen so you can see the pattern quickly.)

Your turn

Find the simple interest and total for $500 at 3% for 4 years.

Find the amount for $500 at 3% compounded annually for 4 years.

$800 is saved at 5% compounded annually. Find the balance after 1, 2 and 3 years.

Write the formula and find the amount for $1 500 at 6% compounded annually for 10 years.

For the $1 500 at 6% for 10 years, how much more is compound interest than simple interest?

Find the simple interest on $1 200 at 4.5% for 3 years.

After how many years do simple and compound interest (compounded annually) give the same amount? Why?

More practice: warm-up

Find the simple interest on $100 at 10% for 1 year.

Find the simple interest and total for $400 at 5% for 2 years.

Write 6% as a decimal.

$100 at 10% compounded annually for 2 years: what is the amount?

Same principal, same rate, 10 years: which earns more, simple or compound interest?

More practice: on your own

$3 000 at 2% for 5 years. Find the simple amount, the compound amount, and the difference.

Find the amount for $2 500 at 6% compounded annually for 4 years.

$600 earns $90 simple interest in 3 years. What is the yearly rate?

A loan of $2 000 at 3% compounded annually is paid back after 2 years in one payment. What is the payment, and how much is interest?

How many years does it take $1 000 at 4% simple interest to earn $200?

Challenge

A bank pays 6% a year compounded monthly, which means 0.5% each month. Find the amount for $1 000 after 1 year. Compare with 6% compounded once a year.

Which is better for $5 000 over 10 years: 4.2% simple interest, or 4% compounded annually? By how much?

A debt of $1 000 grows at 20% compounded annually with no payments. After how many whole years is it more than double?

Check your understanding

Quiz

What is the simple interest on $1 500 at 4% for 3 years?

Which expression gives the amount for $700 at 5% compounded annually for 6 years?

$1 000 at 10% compounded annually for 3 years grows to:

Why does compound interest grow faster than simple interest?

What is 3.5% as a decimal?

For a debt, compound interest is:

For parents and teachers

Big idea: F1.4 asks Grade 8 students to determine the growth of simple and compound interest at various rates. Students use I = P × r × t for simple interest and A = P(1 + r)ⁿ for interest compounded once a year, building on Grade 7's year-by-year calculations and exponents. The next lesson uses spreadsheets to explore long-term growth.

How to help at home:

Make sure your child can use the exponent key on a calculator or phone calculator (turn the phone sideways for a scientific calculator on many phones).
Do the bean activity together and talk about why the compound bowl speeds up.

Common difficulties:

Writing 4% as 0.4. Percent means "out of 100": 4% = 0.04.
Using P × r × t for compound interest, or multiplying by r instead of (1 + r).
Confusing interest with the total amount. Interest is the extra; the amount is principal + interest.
Rounding too early. Small rounding differences of a cent are fine.