An initial investment of $9000 grows at an annual interest rate of 5% compounded continuously. How long will it take to double the investment?
A) 1 year
B) 14.40 years
C) 13.86 years
D) 14.86 years
E) 13.40 years

Question

Quizplus · Accepted Answer

The formula for continuous compounding is A = Pe^(rt), where A is the ending amount, P is the initial investment, e is Euler's number (approximately 2.71828), r is the annual interest rate, and t is the time in years. We want to find t when A = 2P (double the initial investment). Substituting the given values, we get 2P = 9000e^(0.05t). Dividing both sides by P and taking the natural logarithm, we get ln(2) = 0.05t, which gives t = ln(2)/0.05 ≈ 13.86 years. Therefore, the answer is C (13.86 years).

An Initial Investment of $9000 Grows at an Annual Interest