Simple and compound interest: Graph + 5 Practice Questions

Mia and Jay each put 1,000 dollars into a savings account. Both accounts pay 5% a year, and neither saver adds or takes out money. After 15 years, Mia has 1,750 dollars. Jay has 2,079 dollars. Same money, same rate, same time, yet Jay has 329 dollars more. The only difference is how each bank works out the interest.

Key Term

Interest and simple interest

Interest is the price of borrowing money. For a saver, it’s the reward for saving instead of spending. The amount you save or borrow at the start is the principal.

Simple interest is paid on the principal only. Mia earns 5% of 1,000 dollars, which is 50 dollars, every year. After 15 years she has 1,000 + (15 × 50) = 1,750 dollars.

Jay’s bank pays compound interest: interest on interest. Once a year, the bank adds the interest to his balance (the money in his account). This is called compounding: his interest is compounded yearly. The bank then pays next year’s interest on that bigger balance.

Multiplying by 1.05 adds 5%:

Year 1: 1,000 × 1.05 = 1,050 dollars.
Year 2: 1,050 × 1.05 = 1,102.50 dollars.
Year 3: 1,102.50 × 1.05 ≈ 1,157.63 dollars.

In year 2, Jay earns 52.50 dollars, not 50. The extra 2.50 dollars is interest on his first year’s interest.

Multiply the principal $P$ by $(1 + i)$ once for each of the $n$ years to get the balance $A$ . Here $i$ is the yearly rate as a decimal (5% is 0.05).

Interactive — Simple vs compound: the race

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A 1,000-dollar deposit over 30 years, growing with simple interest and with compound interest at the same yearly rate.

The gap keeps growing because compound interest is paid on a bigger balance each time. Simple interest adds the same amount every year. At 8% for 30 years, simple interest turns 1,000 dollars into 3,400. Compound interest turns it into about 10,063: nearly three times as much.

Trap · Common Misconception

Twice as long isn't just twice the interest

With simple interest, doubling the time doubles the interest. With compound interest, the interest more than doubles. At 8% a year, 1,000 dollars earns about 1,159 dollars of interest in 10 years. In 20 years it earns about 3,661 dollars: more than three times as much.

Tip

Adding interest more often adds a little

Banks can also add interest every month. A rate of 12% a year compounded monthly means 1% each month. On 1,000 dollars, adding interest once gives 1,120 dollars after a year. Adding it monthly gives 1,000 × $1.0 1^{12}$ , about 1,126.83 dollars. That’s 6.83 dollars more, because each month’s interest starts earning interest sooner. On a debt, that means you owe a little more.

Key Term

Real return

Your real return is how much more your savings can buy once rising prices are counted. It is roughly the interest rate minus the inflation rate (how fast prices rise). If your savings earn 5% and prices rise 3%, you can buy only about 2% more.

Check yourself · no marks

Ana puts 4,000 dollars in an account that pays 5% compound interest a year. How much does she have after 2 years? How much more is that than simple interest would give?

Commit to one first. Guessing and being wrong beats reading the answer cold.

Worked Example

Imagine you borrow 1,000 dollars at 20% a year, compounded yearly. You repay nothing until the end of 3 years, then repay everything at once. How much do you repay? Compare it with simple interest.

Practice · 1 / 5

Wrong answers cost no XP

Check your understanding of simple and compound interest:

You put 5,000 dollars in an account that pays 6% simple interest a year. You leave it there for 4 years. What is the balance at the end?

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