When interest is compounded continuously, the rate of change of the amount x of the investment is proportional to the amount present. In this case, the proportionality constant is the annual interest rate r (as a decimal); that is, . If $2,500 is invested at 7%, compounded continuously, what will be the future value of this investment after 12 years? Round to the nearest cent.

Question

When interest is compounded continuously, the rate of change of the amount x of the investment is proportional to the amount present. In this case, the proportionality constant is the annual interest rate r (as a decimal); that is,  . If $2,500 is invested at 7%, compounded continuously, what will be the future value of this investment after 12 years? Round to the nearest cent. ​

Quizplus · Accepted Answer

We can use the formula for continuous compounding: $A = Pe^{rt}$ where A is the future value, P is the principal, e is the mathematical constant approximately equal to 2.71828, r is the annual interest rate as a decimal, and t is the time in years.

Plugging in the given values, we get:

$A = 2500e^{0.07(12)}$
$A = 2500e^{0.84}$
$A =$ $5790.92

Rounding to the nearest cent, we get the answer as $5,790.92$, which is option E.

When Interest Is Compounded Continuously, the Rate of Change of the Amount