Simple Interest

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The Simple Interest Formula

Simple interest is calculated using the formula:

\(I = \dfrac{P \times R \times T}{100}\)

where P = Principal (the amount invested or borrowed), R = Rate (the annual interest rate as a percentage), and T = Time (in years).

With simple interest, the same amount of interest is earned every year — it is always calculated on the original principal, not on the growing total.

💡 Worked Example 1 — £500 at 3% for 4 Years

Find the simple interest on £500 invested at 3% per year for 4 years.

Step 1 — Identify the values

P = £500, R = 3, T = 4

Step 2 — Substitute into the formula

\(I = \dfrac{500 \times 3 \times 4}{100} = \dfrac{6000}{100} = \) £60

Step 3 — Total amount

Total = £500 + £60 = £560

\(I = \frac{500 \times 3 \times 4}{100} = \pound60\) Total = £560

💡 Worked Example 2 — £1,200 at 4.5% for 2 Years

Calculate the simple interest on £1,200 at 4.5% per year for 2 years.

Step 1 — Identify the values

P = £1,200, R = 4.5, T = 2

Step 2 — Substitute into the formula

\(I = \dfrac{1200 \times 4.5 \times 2}{100} = \dfrac{10800}{100} = \) £108

\(I = \frac{1200 \times 4.5 \times 2}{100} = \pound108\)

💡 Worked Example 2b — Time given in months

Calculate the simple interest on £900 at 6% per year for 8 months.

Step 1 — Convert months to years

T must be in years: \(8 \text{ months} = \dfrac{8}{12} = 0.6\overline{6}\) years (keep the full decimal, don't round yet)

Step 2 — Substitute into the formula

P = £900, R = 6, T = 8/12: \(I = \dfrac{900 \times 6 \times \frac{8}{12}}{100} = \dfrac{3600}{100} = \) £36

Keeping T as the fraction \(\frac{8}{12}\) rather than a rounded decimal avoids losing accuracy — here it cancels neatly, but it won't always.

✓ Quick Check 1 — The Simple Interest Formula

Question 1 of 10

Finding the Total Amount

Once you have calculated the interest \(I\), you can find the total amount (sometimes called the final amount or amount due) by adding the interest to the principal:

\(\text{Total Amount} = P + I\)

This can also be written as \(A = P + \dfrac{PRT}{100}\), or more compactly as \(A = P\!\left(1 + \dfrac{RT}{100}\right)\).

Total Amount (A) = Principal (P) + Interest (I) or A = P + PRT/100

💡 Worked Example 1 — Savings at 5% for 3 Years

Find the total amount when £1,000 is invested at 5% simple interest per year for 3 years.

Step 1 — Calculate the interest

\(I = \dfrac{1000 \times 5 \times 3}{100} = \dfrac{15000}{100} = \) £150

Step 2 — Add to the principal

Total = £1,000 + £150 = £1,150

I = £150 Total Amount = £1,150

💡 Worked Example 2 — Savings Account at 2.5% for 5 Years

You invest £800 in a savings account paying 2.5% simple interest per year for 5 years. What is the total amount in the account at the end?

Step 1 — Calculate the interest

\(I = \dfrac{800 \times 2.5 \times 5}{100} = \dfrac{10000}{100} = \) £100

Step 2 — Add to the principal

Total = £800 + £100 = £900

Interest earned = £100 Total in account = £900

Note: each year the account earns £100 ÷ 5 = £20. The same £20 is added every year because simple interest is always based on the original £800.

✓ Quick Check 2 — Finding the Total Amount

Question 1 of 10

Rearranging — Finding Rate, Time or Principal

The formula \(I = \dfrac{PRT}{100}\) can be rearranged to find any one of the four variables if the other three are known:

Find R: \(\displaystyle R = \frac{100 \times I}{P \times T}\)
Find T: \(\displaystyle T = \frac{100 \times I}{P \times R}\)
Find P: \(\displaystyle P = \frac{100 \times I}{R \times T}\)

In each case, multiply \(I\) by 100, then divide by the product of the other two variables.

💡 Worked Example 1 — Finding the Rate

£500 was invested for 3 years and earned £75 in simple interest. Find the annual rate of interest.

Step 1 — Write down what you know

P = £500, T = 3, I = £75, R = ?

Step 2 — Use the rearranged formula

\(R = \dfrac{100 \times I}{P \times T} = \dfrac{100 \times 75}{500 \times 3} = \dfrac{7500}{1500} = \) 5%

\(R = \frac{100 \times 75}{500 \times 3} = \frac{7500}{1500} = 5\%\)

💡 Worked Example 2 — Finding the Time

£800 is invested at 4% simple interest per year. It earns £128 in interest. For how many years was it invested?

Step 1 — Write down what you know

P = £800, R = 4, I = £128, T = ?

Step 2 — Use the rearranged formula

\(T = \dfrac{100 \times I}{P \times R} = \dfrac{100 \times 128}{800 \times 4} = \dfrac{12800}{3200} = \) 4 years

\(T = \frac{100 \times 128}{800 \times 4} = \frac{12800}{3200} = 4 \text{ years}\)

💡 Worked Example 3 — Finding the Principal

An investment at 5% per year for 3 years earned £90 in simple interest. How much was originally invested?

Step 1 — Write down what you know

R = 5, T = 3, I = £90, P = ?

Step 2 — Use the rearranged formula

\(P = \dfrac{100 \times I}{R \times T} = \dfrac{100 \times 90}{5 \times 3} = \dfrac{9000}{15} = \) £600

\(P = \frac{100 \times 90}{5 \times 3} = \frac{9000}{15} = \pound600\)

✓ Quick Check 3 — Rearranging the Formula

Question 1 of 10

Practice: Simple Interest Calculations

Use \(I = PRT \div 100\) to calculate the interest for each row. Type your answer in pounds, then click Check.

#	Question	Answer	Result
1	£500 at 3% for 2 years
2	£1,000 at 5% for 3 years
3	£2,000 at 2% for 4 years
4	£750 at 4% for 1 year
5	£600 at 6% for 5 years
6	£900 at 4% for 2 years
7	£1,500 at 3% for 2 years
8	£300 at 5% for 3 years
9	£2,500 at 2% for 1 year
10	£1,200 at 6% for 2 years

⚠ Things to Watch Out For

Using the wrong formula: Simple Interest = (P × R × T) ÷ 100 (where R is a percentage). Do not use the compound interest formula here.
Returning principal + interest vs just interest: The question may ask for total amount (P + I) or just the interest (I) alone. Read carefully and give the right value.
Not converting time to years: T must be in YEARS. 6 months = 0.5 years. 18 months = 1.5 years. Using months directly without conversion gives the wrong answer.
Treating simple interest as compound: In simple interest, interest is calculated on the ORIGINAL principal every period — it does not grow. Don't add interest to the principal for the next year's calculation.
Rate as a decimal vs percentage: In the formula I = PRT/100, R is the percentage (e.g. 5). If you use R = 0.05 instead, omit the ÷100.

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Learning Objectives

Real-World Applications

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💡 Worked Example 1 — £500 at 3% for 4 Years

💡 Worked Example 2 — £1,200 at 4.5% for 2 Years

💡 Worked Example 2b — Time given in months

💡 Worked Example 1 — Savings at 5% for 3 Years

💡 Worked Example 2 — Savings Account at 2.5% for 5 Years

💡 Worked Example 1 — Finding the Rate

💡 Worked Example 2 — Finding the Time

💡 Worked Example 3 — Finding the Principal

Practice: Simple Interest Calculations

⚠ Things to Watch Out For