Simple Interest

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Quick recall

• P = principal; R = annual rate stated as a percentage; T = time in years.
• Convert months to years before substituting.

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Formula Cards

1. Simple interest

$$SI=\frac{PRT}{100}$$

P = principal; R = annual percentage rate; T = years.

2. Amount

$$A=P+SI$$

3. Find principal

$$P=\frac{100\,SI}{RT}$$

4. Find rate

$$R=\frac{100\,SI}{PT}$$

5. Find time

$$T=\frac{100\,SI}{PR}$$

Worked Examples

Example 1

Question: Find SI on Rs. 10,000 at 10% per year for 2 years.

Step 1: Substitute into the simple-interest formula.

$$SI=\frac{10000\times10\times2}{100}$$

Step 2: Calculate.

$$SI=2000$$

Answer: Rs. 2,000.

Example 2

Question: SI is Rs. 600 at 6% per year for 4 years. Find P.

Step 1: Rearrange for the principal.

$$P=\frac{100\,SI}{RT}$$

Step 2: Substitute and calculate.

$$P=\frac{100\times600}{6\times4}=2500$$

Answer: Rs. 2,500.

Example 3

Question: Rs. 5,000 becomes Rs. 6,500 in 3 years under SI. Find the annual rate.

Step 1: Separate interest from amount.

$$SI=6500-5000=1500$$

Step 2: Calculate the annual percentage rate.

$$R=\frac{100\times1500}{5000\times3}=10$$

Answer: 10% per year.

Drill

Try each question before opening its answer.

Question 1

P=8000, R=5%, T=3. Find SI.

• Show answer

  1200

Question 2

Find amount if P=15000, R=8%, T=2.

• Show answer

  17400

Question 3

SI=900, R=6%, T=5. Find P.

• Show answer

  3000

Question 4

P=4000 becomes 5200 in 4 years. Find rate.

• Show answer

  7.5%

Question 5

In how many years will P=2000 give SI=800 at 10%?

• Show answer

  4 years

Question 6

Find SI on Rs.12000 for 2 years 6 months at 8% p.a.

• Show answer

  2400

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