 # Compound Interest Formula

Compound interest formula is mentioned and explained here along with a solved example. To recall, compound interest can be defined as “An interest of interest to the principal sum of a loan or deposit.” In simple words, the compound interest is the interest that adds back to the principal sum, so that interest is earned during the next compounding period. ## Compound Interest Formula

The formula for the Compound Interest is,

$Compound\;Interest\,=\,P(1+\frac{r}{n})^{nt}\,-\,P$

This is the total compound interest which is just the interest generated minus the principal amount. For the total accumulated wealth (or amount), the formula is given as:

$A\,=\,P(1+\frac{r}{n})^{nt}$

### Notations in C.I. Formula:

 C.I. Compound Interest P Principal Amount A Total Accumulated Amount r Rate of Interest n Compounding Frequency Per Annum t Time (in Years)

Note: If the compounding frequency per annum is 1 i.e. if the interest is compounded annually, the compound interest formula is given as:

$C.I.\,=\,P(1+\frac{r}{100})^{t}\,-\,P$

Also Check: Simple Interest Formula

### Example Question Based on C.I. Formula

Question: A sum of Rs. 50,000 is borrowed and the rate of interest is 10% per annum. What is the compound interest for 5 years?

Solution:

From the formula for compound interest, we know,

C.I = P(1+R⁄100)t – P

Here, P = 50,000 ; R = 10% ; T = 5 years ; C.I=?

So, Compound Interest will be-

C.I. = 50000(1+10⁄100)5 – 50000 = 80525.50 – 50000

So, compound interest will be Rs. 30525.50 while the total accumulated wealth (A) will be Rs. 80525.50 at the end of 5 years with an interest rate of 5% per annum.