Now let's consider how this process could be simplified. If we notice that each year we calculate interest on the original principal and all accumulated interest, we could rewrite our calculations like this:

For Year 1, we have $2,000 + (.03 • $2,000), which can also be written like this:

$2,000(1.03) = $2,060

For Year 2, we multiply the whole amount again by 1.03:

$2,000(1.03)(1.03) = $2,121.80

For Year 3, we again multiply by 1.03:

$2,000(1.03)(1.03)(1.03) = $2,185.45

Do you notice a pattern emerging? Using exponential notation, we could write the result for Year 3 as 2000(1.03)³. Generalizing it further, we can write:

value = principal(1 + interest rate)^{number of years}

This formula allows quick calculation of a future value, without having to get an answer for each year in order to calculate the next year.

  Evaluate different investment options