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

The formula for continuous compounding is:

x = ae^(rt)

Where:
x = amount of investment after t years
a = initial investment amount
r = annual interest rate (as a decimal)
t = time in years

Substituting the given values, we get:

x = 2500e^(0.07*12)
x = 2500e^0.84
x = 2500*2.31798
x = 5792.45

Rounding to the nearest cent, we get:

x = $5,790.92

Therefore, the best choice is E.

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