An initial investment of $6000 grows at an annual interest rate of 7% compounded continuously. How long will it take to double the investment?
A)9.90 years
B)1 year
C)10.29 years
D)10.90 years
E)9.29 years

Question

Quizplus · Accepted Answer

The formula for continuous compounding is A = Pe^(rt), where A is the final amount, P is the initial investment, e is the base of the natural logarithm, r is the annual interest rate, and t is the time in years.In this case, we have P = $6000, r = 7%, and A = 2P = $12000. Substituting these values into the formula, we get:12000 = 6000e^(0.07t)Dividing both sides by 6000, we get:2 = e^(0.07t)Taking the natural logarithm of both sides, we get:ln(2) = 0.07tDividing both sides by 0.07, we get:t = ln(2)/0.07 ≈ 9.90 yearsTherefore, it will take approximately 9.90 years to double the investment.

An Initial Investment of $6000 Grows at an Annual Interest