What is the formula for continuous compound interest?

Compound interest is usually calculated at set intervals, such as daily, monthly, or annually. But what if interest is theoretically compounded an infinite number of times? This leads to the concept of continuous compounding.

The continuous compounding formula is used when a question specifies ""compounded continuously"".

This formula involves the mathematical constant 'e', approximately 2.71828.

The formula for continuous compound interest is:

A = Pert

Where:

A = The total accumulated amount, including interest

P = The initial principal amount

e = The mathematical constant e (approx. 2.71828)

r = The annual interest rate expressed as a decimal

t = Time in years

Preeti invested ₹50,000 in a bank that offers an annual interest rate of 8% compounded continuously.

What total amount can she get from the bank after 5 years?

Substituting the values:

P = ₹50,000

r = 8% = 0.08

t = 5 years

Therefore:

A = 50,000 x e0.08x5

A = ₹67,793 (rounded to the nearest integer)

If Preeti invested ₹50,000 at an 8% interest rate compounded continuously, she would accumulate ₹67,793 after 5 years. The continuous compounding formula helps calculate the future value easily.