## Continuous Compound Interest Calculator :

Enter the continuous compound interest calculator its Initial balance in ₹, Interest rate in percentage(%), and you get the calculation below the calculator you check it.

## Continuous Compound Interest Formula :

Amount of money after a certain amount of time A is equal to the product of the P Principle or the amount of money you start with the multibly by the Napier’s number, which is approximately 2.7183.Hence the continuous compound interest formula has been written as,

**A = P * e ^{rt}**

Where,

A →Amount of money after a certain amount of time

P →Principle or the amount of money you start with

e→ Napier’s number, which is approximately 2.7183

r → Interest rate and is always represented as a decimal

t → Amount of time in years

## Sample Examples :

### Example 1:

Calculate the balance after 5 years? In a amount of Rs. 3000 is deposited in a bank paying an annual interest rate of 7%, compounded continuously.

### Solution :

To find: The amount after 5 years.

The initial amount is P = 3000.

The interest rate is, r = 7% = 7/100 = 0.07.

Time is, t = 5 years.

Substitute these values in the continuous compounding formula,

A = Pe^{rt}

A = 3000 * e^{0.07(5)} ≈ 4257

The answer is calculated using the calculator and is rounded to the nearest integer.

The amount after 5 years = 4,257.

### Example 2:

Calculate the paying an annual interest rate ? In a amount of Rs. 5300 is deposited in a bank, the balance after 8 years.

### Solution :

To find: The rate of interest, r.

The initial amount is, P = 5,300.

The final amount is, A = 2(5300) = 10,600.

Time is, t = 8 years.

Substitute all these values in the continuous compound interest formula,

A = Pe^{rt }

10600 = 5300 * e^{r (8)}

Dividing both sides by 5300,

2 = e^{8r}

Taking “ln” on both sides,

ln 2 = 8r

Dividing both sides by 8,

r = (ln 2) / 8 ≈ 0.087 (using calculator)

So the rate of interest = 0.087 * 100 = 8.7

The rate of interest = 8.7%.