Simple Interest

When you put money in a savings account, the bank pays you a little extra for letting them look after it. That extra is called interest, and it is worked out as a percentage of the amount you started with. The amount you start with has a special name — the principal.

With simple interest the bank pays you the same amount every year, because the interest is always a percentage of the original principal — never of the growing balance. If the rate is r (a percentage per year), the principal is P, and the money is left for t years, then the interest is:

I = P \times \frac{r}{100} \times t

People often write the rate as a decimal instead — a rate of 5\% becomes 0.05 — and then the formula is simply I = P\times r \times t. Either way, turn the percent into a decimal (or divide by 100) before you multiply.

To find the total in the account at the end, add the interest back onto the principal:

\text{total} = P + I

This is the "no compounding" cousin of compound interest: with simple interest the interest never earns interest of its own, so the balance climbs by the same fixed step every single year.

One amount as a percent of another

A closely related skill is asking how big one amount is compared to another — "£3 off a £12 pizza is what percent?", "I got 18 out of 20, what percent is that?". You divide the part by the whole and multiply by 100:

A \text{ as a percent of } B = \frac{A}{B} \times 100\%

For example, 18 out of 20 is \tfrac{18}{20}\times 100\% = 90\%, and a \pounds 3 discount on a \pounds 12 pizza is \tfrac{3}{12}\times 100\% = 25\% off. This is exactly how you would work out interest as a percentage of your savings, or a percentage of an amount the other way round.

Three worked examples

Find the interest. You save \pounds 400 at 5\% simple interest for 3 years. The interest is I = 400\times\tfrac{5}{100}\times 3 = \pounds 60 — that is \pounds 20 each year, three times.
Find the total. Same account, so the money in the bank after 3 years is P + I = 400 + 60 = \pounds 460.
One amount as a percent of another. A jumper is \pounds 15 off its original \pounds 60 price. As a percent of the original that discount is \tfrac{15}{60}\times 100\% = 25\% off.

For a principal P at a rate of r\% per year, over t years:

the interest is I = P \times \tfrac{r}{100} \times t;
the total is P + I;
it is the same amount each year, always a percent of the original principal — it does not compound;
one amount as a percent of another is \tfrac{A}{B}\times 100\%.

Two traps to dodge:

Simple interest is the same every year, worked out on the original principal — never on the growing balance. If you take a percent of the new total each year, that is compound interest, a different (and faster-growing) thing.
Turn the percent into a decimal before you multiply. 5\% is 0.05, not 5 — forgetting to divide by 100 makes the interest a hundred times too big.

coin

Drop \pounds 100 into a piggy bank that pays 10\% simple interest. Every birthday the bank hands you \tfrac{10}{100}\times 100 = \pounds 10 — the same \pounds 10 coin each year, because it is always 10\% of your original \pounds 100. After 4 years you have collected 4\times 10 = \pounds 40 of interest, so the bank holds \pounds 140.

scales

Percent is really a pair of scales: it weighs one amount against another. "£40 of interest on £100 of savings" balances out to \tfrac{40}{100}\times 100\% = 40\%. Turning two numbers into a single percent lets you compare deals that started from different amounts — the same trick as working out a test score or a discount as a percentage.

See it: the same step every year

Each bar is the money in the account at the end of a year. The bottom block is the principal; on top sit the years of interest — and every one of those interest blocks is exactly the same height, because simple interest adds the same amount each year. Press Play to grow it year by year, or Refresh for a new savings pot.