An initial investment of $3000 doubles in value in 8.3 years. Assuming continuous compounding, what was the interest rate? Round to the nearest tenth of a percent.
A) 8.4%
B) 3.6%
C) 4.2%
D) 8.3%
E) 100%

Question

Quizplus · Accepted Answer

The formula for continuous compounding is A = Pe^(rt), where A is the final amount, P is the initial amount, e is the base of the natural logarithm, r is the interest rate, and t is the time. We can use this formula to solve for r:3000 = 3000e^(8.3r)e^(8.3r) = 28.3r = ln(2)r = ln(2)/8.3r ≈ 0.084Therefore, the interest rate is approximately 8.4%.

An Initial Investment of $3000 Doubles in Value in 8