Choose the one alternative that best completes the statement or answers the question.
-If Emery has $1,100 to invest at 9% per year compounded monthly, how long will it be before he has $1,400? If the compounding is continuous, how long will it be? (Round your answers to three decimal places.)
A) 0.036 yrs, 0.268 yrs
B) 66.89 yrs, 2.902 yrs
C) 2.69 yrs, 2.68 yrs
D) 0.233 yrs, 0.223 yrs

Question

Quizplus · Accepted Answer

For the first part, when the compounding is monthly, the formula to use is $A = P(1 + \frac{r}{n})^{nt}$, where $A$ is the amount of money accumulated after n years, including interest, $P$ is the principal amount (the initial amount of money), $r$ is the annual interest rate (decimal), $n$ is the number of times that interest is compounded per year, and $t$ is the time the money is invested for in years. For the second part, when the compounding is continuous, the formula to use is $A = Pe^{rt}$, where $e$ is the base of the natural logarithm, approximately equal to 2.71828. By solving these equations with the given values ($P = 1100$, $A = 1400$, $r = 0.09$), we can find the time $t$ for both scenarios. The correct answer reflects the time calculated using both methods, showing that it takes approximately 2.69 years with monthly compounding and approximately 2.68 years with continuous compounding to grow $1,100 to $1,400 at a 9% annual interest rate.

Choose the One Alternative That Best Completes the Statement or Answers