Question

If $1000 is invested at an interest rate of 3.5% per year, compounded continuously, find the value of the investment after the given number of years. (round your answers to the nearest cent.)

Answer 1

The key words here are compounded continuously. That being said let's use the continuous growth formula:

$a(t) = p {e}^{rt}$
where a(t) is the final amount after t years, p is the principal amount (starting amount $1000), r is the rate in decimal 3.5% = 0.035. And so for any given year the final amount can be described as:

$a(t) = 1000 {e}^{0.035t}$