Compound Interest formula:
story, analogy and memory trick
The Compound Interest formula is A = P × (1 + r/100)ⁿ. With compound interest, each year's interest is added to the principal, so the amount after n years is P times (1 + r/100) raised to the power n.
The Compound Interest formula
- Atotal amount after n years
- Pprincipal, the money you start with
- rrate of interest per year, in percent
- nnumber of years
The story
Aman deposits Rs 10,000 at 10% a year. After year one the bank adds Rs 1,000. In year two it pays interest on Rs 11,000, not Rs 10,000, so the total becomes Rs 12,100. Each year the money earns on its earlier earnings too, like a snowball growing as it rolls.
Real-life analogy
Think of a snowball rolling downhill. It picks up more snow with every turn, and the bigger it gets, the faster it grows.
Memory trick
Say 'principal times growth factor, n times'. The growth factor is 1 plus the rate as a fraction. Then CI = A − P.
Exam tip
For half-yearly compounding use rate r/2 and 2n periods, and for quarterly use r/4 and 4n. Compound interest is the amount minus the principal. For 2 years, CI = P × (r/100) × (2 + r/100).
Questions about Compound Interest
What is the Compound Interest formula?
How do I remember the Compound Interest formula?
What should I watch out for in exams with Compound Interest?
More Maths formulas
Quadratic
x = (−b ± √(b² − 4ac)) ÷ 2a
It gives the roots of any quadratic equation ax² + bx + c = 0 using only its three coefficients.
Read the storyPythagoras Theorem
a² + b² = c²
In a right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides.
Read the storyBasic Trigonometric Identity
sin²θ + cos²θ = 1
For any angle θ, the square of the sine plus the square of the cosine is always equal to 1.
Read the storyNeed a story for a different formula?
Type any formula or topic into the free ThunderStudy AI tool and get a story, a real-life analogy or a memory trick.