Simple Interest

Simple interest is the money earned (or owed) found by multiplying the starting amount by the rate and the time.

I = P × r × t

The principal stays fixed. The same interest amount is added for each year.

What each symbol means

• I: the interest (the extra money earned or charged)
• P: the principal (the starting amount of money)
• r: the rate per year, written as a decimal (5% becomes 0.05)
• t: the time in years

When you keep money in a savings account, or borrow money for a loan, extra money gets added on top. That extra is called interest. Simple interest is the most basic version: the same amount is added every year, based only on the starting amount.

The formula is I = P × r × t. Multiply how much you started with, by the yearly rate, by the number of years.

Turn the percent into a decimal first: A rate like 5% means 5 out of 100, which is 0.05. Always convert the percent to a decimal before you multiply. Move the point two places left.

A worked example

You save \$1000 at 5% simple interest for 3 years

1. Write the formula: I = P × r × t.
2. Change the rate to a decimal: 5\% = 0.05.
3. Put in the numbers: I = 1000 × 0.05 × 3.
4. Multiply: 1000 × 0.05 = 50, then 50 × 3 = 150.
5. You earn \150 in interest. The account now holds1000 + 150 = 1150$ dollars.

Interest vs total: The formula gives the interest only. To get the final total, add it back to the principal: total = P + I.

• Simple interest is I = P × r × t.
• Convert the percent rate to a decimal before multiplying.
• The same interest is added each year, because it is always based on the original amount.
• The final total is the principal plus the interest.

Why it is principal times rate times time

1. In one year, the interest earned is the rate applied to the principal: P × r.
2. For example, 5% of \1000 is0.05 \times 1000 = 50$ dollars per year.
3. With simple interest, that same amount is added every year (it always uses the original principal, never the growing balance).
4. So over t years the interest is that yearly amount repeated t times: P × r × t.

Practice questions

Question 1

Find the simple interest on \$2000 at 4% for 2 years.

1. Write the formula: I = P × r × t.
2. Change the rate to a decimal: 4\% = 0.04.
3. Put in the numbers: I = 2000 × 0.04 × 2.
4. Multiply step by step: 2000 × 0.04 = 80, then 80 × 2 = 160.
5. The interest is \$160.

Answer: \$160

Question 2

Find the simple interest on \$500 at 6% for 3 years.

1. Write the formula: I = P × r × t.
2. Change the rate to a decimal: 6\% = 0.06.
3. Put in the numbers: I = 500 × 0.06 × 3.
4. Multiply step by step: 500 × 0.06 = 30, then 30 × 3 = 90.
5. The interest is \$90.

Answer: \$90

Question 3

You borrow \$1500 at 10% simple interest for 1 year. How much interest do you owe?

1. Write the formula: I = P × r × t.
2. Change the rate to a decimal: 10\% = 0.10.
3. Put in the numbers: I = 1500 × 0.10 × 1.
4. Multiply: 1500 × 0.10 = 150, and times 1 is still 150.
5. You owe \$150 in interest.

Answer: \$150

Question 4

A \1000 deposit earns \200 simple interest over 4 years. What is the yearly rate?

1. Start from the formula: I = P × r × t.
2. Put in what you know: 200 = 1000 × r × 4.
3. Combine the numbers on the right: 200 = 4000r.
4. Divide both sides by 4000: r = 2004000 = 0.05.
5. Turn the decimal back into a percent: 0.05 = 5\%.

Answer: 5\%

Question 5

What is the total balance after earning \80 interest on a \1000 deposit?

1. The total is the starting amount plus the interest earned: total = P + I.
2. The principal is \1000 and the interest is \80.
3. Add them: 1000 + 80 = 1080.
4. The total balance is \$1080.

Answer: \$1080