About Simple Interest
Simple interest is one multiplication: principal times rate times time, divided by 100. The formula itself rarely causes trouble — the marks are lost on rearranging it and on telling apart the interest from the total amount.
What you need to understand
- Simple interest is charged only on the original principal, so it grows in a straight line rather than compounding.
- The rate is always quoted per annum, so a time given in months or days must be converted to years first.
- The amount is the principal plus the interest, not the interest alone.
- Given any three of principal, rate, time and interest you can find the fourth by rearranging the same formula.
- Doubling the time doubles the simple interest; doubling the rate does the same. The relationship is proportional.
- Compound interest works differently, because it charges interest on interest already earned.
Formulas to remember
How to work through these questions
- Write down the four quantities P, R, T and SI, and mark which three the question gives you.
- Convert the time to years if it is given in months, and divide the rate by 100 early so it stops being a percentage.
- Substitute into the formula and simplify the numbers before multiplying them together.
- If the question asks for the amount, add the principal back at the end.
- Sanity-check the size: a modest rate over a short time should give interest well below the principal.
Mistakes that cost marks
- Forgetting to divide by 100 after multiplying principal, rate and time.
- Using a time given in months directly as though it were years.
- Answering with the interest when the question asks for the amount, or the other way round.
- Treating the amount as the principal when working out the rate or the time.
- Applying the compound-interest formula to a simple-interest question.
Worked example
Find the simple interest on Rs. 5000 at 8% per annum for 3 years.
- Write down what is given: P = 5000, R = 8, T = 3.
- Substitute into SI = (P x R x T) / 100 = (5000 x 8 x 3) / 100.
- Simplify before multiplying: 5000 / 100 = 50, so the sum becomes 50 x 8 x 3.
- 50 x 8 x 3 = 1200.
Answer: Rs. 1200
Practice questions with answers
A few Simple Interest questions with the full solution shown, so you can see
how the method is applied before you attempt the timed set.
Question 1
What is the simple interest on a sum of Rs. 600 for 2 years at 5% per annum?
Answer: Option D — with explanation
Simple interest = (P x R x T) / 100.
= (600 x 5 x 2) / 100 = 60.
Common mistakes
- divided by 1000 instead of 100: 6
- gave the total amount instead of the interest: 660
- forgot to divide by 100: 6000
Question 2
A sum of Rs. 1400 is invested at 10% simple interest per annum for 7 years. Find the total amount.
-
A
980
-
B
98000
-
C
2380
-
D
2383
Answer: Option C — with explanation
Interest = (P x R x T) / 100 = (1400 x 10 x 7) / 100 = 980.
Amount = principal + interest = 1400 + 980 = 2380.
Common mistakes
- gave the interest only, not the total amount: 980
- forgot to divide the interest by 100: 98000
- an arithmetic slip in the final step: 2383
Question 3
The simple interest on Rs. 500 for 7 years is Rs. 140. Find the rate per cent per annum.
Answer: Option D — with explanation
SI = (P x R x T) / 100, so R = (SI x 100) / (P x T).
R = (140 x 100) / (500 x 7) = 4% per annum.
Common mistakes
- multiplied by the time instead of dividing: 196
- forgot to divide by the number of years: 28
- treated the interest itself as the rate: 20
Question 4
What is the simple interest on a sum of Rs. 1100 for 4 years at 8% per annum?
-
A
352
-
B
35200
-
C
35.2
-
D
1452
Answer: Option A — with explanation
Simple interest = (P x R x T) / 100.
= (1100 x 8 x 4) / 100 = 352.
Common mistakes
- forgot to divide by 100: 35200
- gave the total amount instead of the interest: 1452
- divided by 1000 instead of 100: 35.2
Question 5
A sum of Rs. 1900 is invested at 5% simple interest per annum for 7 years. Find the total amount.
-
A
2562
-
B
665
-
C
2565
-
D
66500
Answer: Option C — with explanation
Interest = (P x R x T) / 100 = (1900 x 5 x 7) / 100 = 665.
Amount = principal + interest = 1900 + 665 = 2565.
Common mistakes
- forgot to divide the interest by 100: 66500
- gave the interest only, not the total amount: 665
- an arithmetic slip in the final step: 2562
Frequently asked questions
What is the difference between interest and amount?
Interest is only the charge for borrowing the money. The amount is the interest plus the original principal, so it is the total that has to be repaid.
Do I need to convert months into years?
Yes. The rate is per annum, so a time of 8 months is 8/12 of a year. Using 8 directly gives an answer eight times too large.
How is simple interest different from compound interest?
Simple interest is calculated only on the original principal every year. Compound interest is calculated on the principal plus the interest already added, so it grows faster.
How do I find the rate when I know the interest?
Rearrange the formula to R = (SI x 100) / (P x T). The interest of Rs. 500 on Rs. 1000 over 5 years gives R = (500 x 100) / (1000 x 5) = 10% per annum.
