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.
A)$4,600.00
B)$5,776.80
C)$5,630.48
D)$5,708.32
E)$5,790.92

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. ​
A)$4,600.00 
B)$5,776.80 
C)$5,630.48 
D)$5,708.32 
E)$5,790.92

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