How long will it take for $8400 to grow to $14.600 at an interest rate of 9.4% if the interest is compounded continuously? Round the number of years to the nearest hundredth.
A)5.88 yr
B)58.81 yr
C)0.59 yr
D)0.06 yr

Question

Quizplus · Accepted Answer

The correct answer is A because the formula for continuous compounding is A = Pe^(rt), where A is the final amount, P is the principal, e is the base of the natural logarithm, r is the annual interest rate, and t is the time in years. Substituting the given values into the formula, we get 14600 = 8400e^(0.094t). Dividing both sides by 8400, we get e^(0.094t) = 1.7381. Taking the natural logarithm of both sides, we get 0.094t = 0.5605. Dividing both sides by 0.094, we get t = 5.96 years. Rounding to the nearest hundredth, we get t = 5.88 years.

How Long Will It Take for $8400 to Grow to $14.600