Simple and Compound Interest: Formulas and Examples
Interest is the extra money you pay for borrowing, or earn for saving. In Indian school maths (Class 8 to 10) and in aptitude tests for banking and competitive exams, two types matter most: simple interest and compound interest. This guide gives you both formulas, the crucial difference between them, and worked examples you can follow step by step.
What is simple interest?
Simple interest is calculated only on the original amount you borrow or invest, called the principal. It stays the same every year. The formula is SI = P × R × T / 100.
- P (Principal): the starting amount of money.
- R (Rate): the yearly rate of interest as a percentage.
- T (Time): the number of years.
Example: Find the simple interest on ₹10,000 at 8% per year for 3 years. SI = 10000 × 8 × 3 / 100 = ₹2,400. The total amount to be repaid, called the maturity amount, is P + SI = 10000 + 2400 = ₹12,400.
What is compound interest?
Compound interest is calculated on the principal plus the interest already added. So you earn interest on your interest, which makes money grow faster. The amount is A = P × (1 + R/100)ⁿ, and the compound interest itself is CI = A − P, where n is the number of years.
Example: Find the compound interest on ₹10,000 at 8% per year for 2 years. A = 10000 × (1 + 8/100)² = 10000 × (1.08)² = 10000 × 1.1664 = ₹11,664. So CI = 11664 − 10000 = ₹1,664.
The key difference between SI and CI
Over the same period, compound interest is always equal to or greater than simple interest, because CI keeps adding interest on top of interest. For the first year they are exactly equal; the gap starts from the second year.
Example: Using the same numbers as above, the simple interest for 2 years is SI = 10000 × 8 × 2 / 100 = ₹1,600, while CI was ₹1,664. The difference is ₹64. There is a neat shortcut: for 2 years the difference equals P × (R/100)² = 10000 × (8/100)² = 10000 × 0.0064 = ₹64, which matches exactly.
How to solve interest problems quickly
First read whether the question says simple or compound. Write down P, R and T, then plug into the right formula. For compound interest, remember to find the amount A first and subtract P at the end. Interest sums rely heavily on percentages, so brushing up with our fractions, decimals and percentages guide helps a lot. Learners can strengthen the basics with our Class 9 Maths material, while exam aspirants will find these formulas useful for NDA Maths aptitude sections.
Frequently asked questions
What is the main difference between simple and compound interest?
Simple interest is calculated only on the original principal, so it is the same each year. Compound interest is calculated on the principal plus previously added interest, so the interest amount grows year after year and gives a larger total.
Are simple and compound interest ever equal?
Yes, for a time period of one year at the same rate, simple interest and compound interest give exactly the same value. The difference between them only starts appearing from the second year onward.
What does compounded annually mean?
Compounded annually means the interest is added to the principal once every year. If interest is added more often, such as half-yearly, you adjust the formula by halving the rate and doubling the number of periods.