Simple and Compound Interest

Stage 10 of 23 Strand 7 of 9 4 lessons

4 illustrated lessons, each teaching the why before the how.

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Simple Interest #

The same interest each year, from the start alone.

Simple interest pays the same amount every year, a fixed percent of the starting sum

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Save $200 in a bank and every year it adds 5% of your deposit. That payment is interest.

5% of $200 is $10. Simple interest pays that same $10 every year, on the $200 start.

Three years means three equal payments of $10: the interest comes to $30 in all.

One calculation covers it: principal × rate × years ÷ 100. Here 200 × 5 × 3 ÷ 100 = 30.

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$600 is invested at 4% simple interest per year. How much interest does it earn in 4 years?

$600 is invested at 3% simple interest per year. How much interest does it earn in 4 years?

Compound Interest #

Interest paid on the interest already earned.

Compound interest pays interest on the interest, so the balance grows faster every year

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Now the interest stays in the account — so next year it earns interest of its own.

Year one pays 10% of $1000. That is $100, and the balance grows to $1100.

Year two pays 10% of $1100, not $1000 — $110, because year one’s $100 now earns too.

The balance runs 1000, 1100, 1210, 1331. Every jump is bigger than the one before it.

Each year multiplies the balance by 1.1 — so after n years it is the start times 1.1ⁿ.

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$3000 is invested at 20% a year, compounded yearly. What is the balance after 3 years?

$2000 is invested at 10% a year, compounded yearly. What is the balance after 3 years?

Compounding More Than Once a Year #

Divide the rate, multiply the count of periods.

Compounding k times a year charges r / k each period over k × n periods

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Yearly compounding multiplies the deposit by 1 + r/100 once for every year.

Quarterly compounding pays a quarter of the rate four times a year: 2%, twelve times in three years.

So the rate is divided by k and the number of multiplications becomes k times n.

On $1000 at 8% for 3 years, quarterly reaches $1268.24 against yearly’s $1259.71.

More often pays more, but the gain shrinks: monthly adds only $2 on top of that.

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$5000 is invested at 12% a year, compounded quarterly. What is the balance after 3 years?

$2000 is invested at 4% a year, compounded quarterly. What is the balance after 2 years?

Simple versus Compound Interest #

A straight line against a curve that pulls away.

Simple interest grows by equal steps, compound by steps that keep growing

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Two accounts open with a principal of $1000 at 10% a year: one grows by simple interest (linear), the other by compound (exponential).

The simple account grows by the same $100 every year: $1100, $1200, $1300, a straight line.

The compound account reaches $1100, then $1210, then $1331: the yearly gain grows from $100 to $110 to $121.

After three years it is $1331 against $1300, and the gap between them widens every year.

Now you

$1000 is invested at 10% simple interest per year. What is the balance after 3 years?

$2000 is invested at 10% a year for two years. How much more does compound interest pay than simple interest?

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