For an investment of $1,000 at a 7% interest rate over 100 years with continuous compounding, what is the first step in calculation?

The first step in calculating the future value of an investment with continuous compounding involves understanding the formula used in this context, which is expressed as:

[ FV = Pe^{rt} ]

In this formula, ( P ) represents the principal amount (initial investment), ( r ) is the annual interest rate (expressed as a decimal), ( t ) is the time in years, and ( e ) is the mathematical constant approximately equal to 2.71828.

Considering the scenario given, where the investment is $1,000 at a 7% interest rate for 100 years, the critical first step to successfully apply this formula is to convert the annual interest rate from a percentage to a decimal format. This means taking the 7% rate and expressing it as 0.07 (by dividing by 100), which is vital for the correct application of the formula.

This step lays the groundwork for subsequently calculating ( e ) raised to the power of the product of the interest rate and time, allowing for the proper evaluation of the investment's future value over the specified period of time.