Calculation on Continuous Compounding Formula

Example 1: Suppose you invest Rs 1,000 at an annual interest rate of 5% compounded continuously. What will be the investment after one year?

Solution:

Given we want to invest Rs 1,000 at an annual interest rate of 5% compounded continuously, the future value (FV) can be calculated as follows:

FV = PV x e^{(i x t)}

After one year, the future value (FV) can be calculated as follows:

FV = Rs 1,000 x e^{(0.05 x 1)} ≈ Rs 1,051.27

After one year, your investment would be worth approximately Rs 1,051.27.

Example 2: Suppose you deposit Rs. 5,000 into a savings account with a stated annual interest rate of 4.5% that compounds continuously. How much will you have in the account after 3 years?

Solution:

Given we want to invest Rs. 5,000 into a savings account with a stated annual interest rate of 4.5% that compounds continuously, the future value (FV) can be calculated as follows for three years:

FV = PV x e^{(i x t)}

FV = Rs 5,000 x e^{(0.045 x 3)} ≈ Rs 5,659.47

After 3 years, your savings account would hold approximately Rs 5,659.47.

Example 3: You decide to invest Rs. 12,000 in a savings account with a stated annual interest rate of 4.75% that compounds continuously. How much will your investment be worth after 3 years?

Solution:

Given we want to invest Rs. 12,000 into a savings account with a stated annual interest rate of 4.75% that compounds continuously, the future value (FV) can be calculated as follows for three years:

FV = PV x e^{(i x t)}

FV = Rs 12,000 x e^{(0.0475 x 3)} ≈ Rs 13,764.11

After 3 years, your savings account would hold approximately Rs 13,764.11.

Example 4: You have Rs. 9,500 to invest in a certificate of deposit (CD) with a stated annual interest rate of 5.5% that compounds continuously. How much will you have in the CD after 4 years?

Solution:

Given we want to invest Rs.9,500 into a certificate of deposit (CD) with a stated annual interest rate of 5.5% that compounds continuously, the future value (FV) can be calculated as follows for four years:

FV = PV x e^{(i x t)}

FV = Rs 9,500 x e^{(0.055 x 4)} ≈ Rs 11,048.46

After 4 years, your savings account would hold approximately Rs 11,048.46.

Example 5: You decide to invest Rs. 16,500 in a bond with a stated annual interest rate of 4.25% that compounds continuously. Calculate the future value of your investment after 5 years.

Solution:

Given we want to invest Rs.16,500 with a stated annual interest rate of 4.25% that compounds continuously, the future value (FV) can be calculated as follows for five years:

FV = PV x e^{(i x t)}

FV = Rs 16,500 x e^{(0.0425 x 5)} ≈ Rs 19,438.24

After 4 years, your savings account would hold approximately Rs 19,438.24.

Continuous Compounding Formula is a financial concept where interest is continuously computed and added to an account’s balance over an infinite number of time intervals.

In this article, we will discuss about Continuous compounding formula in detail starting with the continuous compounding formula understanding followed by solved examples and practice problems on the continuous compounding formula.