Formula

Compound interest amount $A = P (1 + \frac{r}{100})^{n}$

Arithmetic • Interest • Compound Interest

Formula

A = P (1 + \frac{r}{100})^{n}

A principal

P

compounded at

r %

per period for

n

periods amounts to

A = P (1 + \frac{r}{100})^{n}

, and the compound interest is

A - P

; the interest belonging to the

k

-th period alone is

P (1 + \frac{r}{100})^{k - 1} \times \frac{r}{100}

How to use it

1Every period multiplies the balance by the same factor $1 + \frac{r}{100}$ , so $n$ periods multiply by that factor $n$ times.
2Most questions ask for the interest, not the amount: subtract $P$ at the end.
3For half-yearly compounding halve the rate and double the number of periods; for quarterly, quarter the rate and quadruple the periods.

Find the amount and the compound interest on Rs

8000

for

2

years at

10%

per annum.

Step-by-step

1
$A = 8000 (1 + \frac{10}{100})^{2} = 8000 \times \frac{11}{10} \times \frac{11}{10}$
Why: Two years, so the factor $\frac{11}{10}$ is applied twice.
2
$A = 9680$ , so $CI = 9680 - 8000 = 1680$
Why: The compound interest is the amount less the principal.

Answer

Amount Rs

9680

, compound interest Rs

1680

Watch out

The rate and the period must match:

10%

per annum compounded half-yearly means

5%

for

4

half-years over

2

years, not

10%

for

2

. And the compound interest is

A - P

, never

A

Builds on

x %

Also known as

compound interest formula, amount formula, P(1+r/100)^n, CI formula, interest of the nth year, compounded annually, compound interest amount