# Future Value of Continuous Compounding Investment

## What is the future value of an investment of $2300 compounded continuously at 2% for 3 years?

Final answer:

Using the formula for continuous compounding, the future value of a $2300 investment at 2% interest compounded continuously for 3 years is approximately $2423.38.

## Answer:

The future value of an investment of $2300 compounded continuously at a rate of 2% for 3 years can be calculated using the formula for continuous compounding, FV = Pert, where P is the principal amount, e is the base of the natural logarithm, r is the annual interest rate, and t is time in years.

To find the future value of an investment with continuous compounding, we apply the formula FV = Pert. Plugging in the values from the question, we have FV = $2300e^(0.02*3).

The number e is an irrational constant approximately equal to 2.71828. Raising e to the power of the product of the interest rate and the time period gives the factor by which the principal will grow. In this scenario, the exponent is 0.02*3 = 0.06.

By raising e to this exponent, we calculate the multi-factor for the growth of the investment over 3 years. When you perform this calculation, the investment will grow to approximately $2423.38, assuming a 2% rate and that the interest is compounded continuously.

Continuous compounding is the theoretical limit of compounding frequency, as if it were happening every moment.

Continuous compounding is a powerful concept in the world of finance. It allows investors to earn interest on their principal amount continuously, leading to higher returns compared to other compounding methods.

When we have an investment of $2300 and it is compounded continuously at an annual interest rate of 2% for 3 years, we can see the magic of exponential growth in action. The formula FV = Pert, where P is the principal amount, e is the base of the natural logarithm, r is the annual interest rate, and t is time in years, helps us calculate the future value of the investment.

In this case, the continuous compounding formula gives us a future value of approximately $2423.38. This means that our $2300 investment will grow by around $123.38 over the span of 3 years, thanks to the power of continuous compounding.

Understanding the principles of continuous compounding can be beneficial for investors looking to maximize their returns over time. By harnessing the concept of compounding interest continuously, one can see their investments grow exponentially, leading to greater wealth accumulation in the long run.

So, next time you come across a scenario involving continuous compounding, remember the formula FV = Pert and the wonders it can do for your investments!