Complete the following chart, which illustrates what happens to $16,000 invested at various rates of interest for different lengths of time but always compounded continuously. Round your answers to the nearest dollar. $$\begin{array} { | c | c | c | c | c | }
\hline & \mathbf { 8 } \% & \mathbf { 1 0 } \% & \mathbf { 1 2 } \% & \mathbf { 1 4 } \% \
\hline 5 \text { years } & & & & \
\hline 8 \text { years } & & & & \
\hline 11 \text { years } & & & & \
\hline 14 \text { years } & & & & \
\hline 17 \text { years } & & & & \
\hline
\end{array}$$
A) $\begin{array} { | c | c | c | c | c | }
\hline & \mathbf { 8 } \% & \mathbf { 1 0 } \% & \mathbf { 1 2 } \% & \mathbf { 1 4 } \% \
\hline 5 \text { years } & 23869 & 26380 & 29154 & 32220 \
\hline 8 \text { years } & 30344 & 35609 & 41787 & 49038 \
\hline 11 \text { years } & 38574 & 48067 & 59895 & 74633 \
\hline 14 \text { years } & 49038 & 64883 & 85849 & 113589 \
\hline 17 \text { years } & 62339 & 87583 & 123050 & 172878 \
\hline
\end{array}$
B) $\begin{array} { | c | c | c | c | c | }
\hline & \mathbf { 8 } \% & \mathbf { 1 0 } \% & \mathbf { 1 2 } \% & \mathbf { 1 4 } \% \
\hline 5 \text { years } & 32220 & 29154 & 26380 & 23869 \
\hline 8 \text { years } & 49038 & 41787 & 35609 & 30344 \
\hline 11 \text { years } & 74633 & 59895 & 48067 & 38574 \
\hline 14 \text { years } & 113589 & 85849 & 64883 & 49038 \
\hline 17 \text { years } & 172878 & 123050 & 87583 & 62339 \
\hline
\end{array}$
C) $\begin{array} { | c | c | c | c | c | }
\hline & \mathbf { 8 } \% & \mathbf { 1 0 } \% & \mathbf { 1 2 } \% & \mathbf { 1 4 } \% \
\hline 5 \text { years } & 47738 & 52759 & 58308 & 64440 \
\hline 8 \text { years } & 60687 & 71217 & 83574 & 98075 \
\hline 11 \text { years } & 77149 & 96133 & 119789 & 149267 \
\hline 14 \text { years } & 98075 & 129766 & 171698 & 227178 \
\hline 17 \text { years } & 124678 & 175166 & 246099 & 345757 \
\hline
\end{array}$
D) $\begin{array} { | c | c | c | c | c | }
\hline & \mathbf { 8 } \% & \mathbf { 1 0 } \% & \mathbf { 1 2 } \% & \mathbf { 1 4 } \% \
\hline 5 \text { years } & 11935 & 13190 & 14577 & 16110 \
\hline 8 \text { years } & 15172 & 17804 & 20894 & 24519 \
\hline 11 \text { years } & 19287 & 24033 & 29947 & 37317 \
\hline 14 \text { years } & 24519 & 32442 & 42924 & 56795 \
\hline 17 \text { years } & 31170 & 43792 & 61525 & 86439 \
\hline
\end{array}$
E) $\begin{array} { | c | c | c | c | c | }
\hline & \mathbf { 8 } \% & \mathbf { 1 0 } \% & \mathbf { 1 2 } \% & \mathbf { 1 4 } \% \
\hline 5 \text { years } & 62339 & 87583 & 123050 & 172878 \
\hline 8 \text { years } & 49038 & 64883 & 85849 & 113589 \
\hline 11 \text { years } & 38574 & 48067 & 59895 & 74633 \
\hline 14 \text { years } & 30344 & 35609 & 41787 & 49038 \
\hline 17 \text { years } & 23869 & 26380 & 29154 & 32220 \
\hline
\end{array}$

Question

Complete the following chart, which illustrates what happens to $16,000 invested at various rates of interest for different lengths of time but always compounded continuously. Round your answers to the nearest dollar. $$\begin{array} { | c | c | c | c | c | } 
\hline & \mathbf { 8 } \% & \mathbf { 1 0 } \% & \mathbf { 1 2 } \% & \mathbf { 1 4 } \% \
\hline 5 \text { years } & & & & \
\hline 8 \text { years } & & & & \
\hline 11 \text { years } & & & & \
\hline 14 \text { years } & & & & \
\hline 17 \text { years } & & & & \
\hline
\end{array}$$
A) $\begin{array} { | c | c | c | c | c | } 
\hline & \mathbf { 8 } \% & \mathbf { 1 0 } \% & \mathbf { 1 2 } \% & \mathbf { 1 4 } \% \
\hline 5 \text { years } & 23869 & 26380 & 29154 & 32220 \
\hline 8 \text { years } & 30344 & 35609 & 41787 & 49038 \
\hline 11 \text { years } & 38574 & 48067 & 59895 & 74633 \
\hline 14 \text { years } & 49038 & 64883 & 85849 & 113589 \
\hline 17 \text { years } & 62339 & 87583 & 123050 & 172878 \
\hline
\end{array}$
B) $\begin{array} { | c | c | c | c | c | } 
\hline & \mathbf { 8 } \% & \mathbf { 1 0 } \% & \mathbf { 1 2 } \% & \mathbf { 1 4 } \% \
\hline 5 \text { years } & 32220 & 29154 & 26380 & 23869 \
\hline 8 \text { years } & 49038 & 41787 & 35609 & 30344 \
\hline 11 \text { years } & 74633 & 59895 & 48067 & 38574 \
\hline 14 \text { years } & 113589 & 85849 & 64883 & 49038 \
\hline 17 \text { years } & 172878 & 123050 & 87583 & 62339 \
\hline
\end{array}$
C) $\begin{array} { | c | c | c | c | c | } 
\hline & \mathbf { 8 } \% & \mathbf { 1 0 } \% & \mathbf { 1 2 } \% & \mathbf { 1 4 } \% \
\hline 5 \text { years } & 47738 & 52759 & 58308 & 64440 \
\hline 8 \text { years } & 60687 & 71217 & 83574 & 98075 \
\hline 11 \text { years } & 77149 & 96133 & 119789 & 149267 \
\hline 14 \text { years } & 98075 & 129766 & 171698 & 227178 \
\hline 17 \text { years } & 124678 & 175166 & 246099 & 345757 \
\hline
\end{array}$
D) $\begin{array} { | c | c | c | c | c | } 
\hline & \mathbf { 8 } \% & \mathbf { 1 0 } \% & \mathbf { 1 2 } \% & \mathbf { 1 4 } \% \
\hline 5 \text { years } & 11935 & 13190 & 14577 & 16110 \
\hline 8 \text { years } & 15172 & 17804 & 20894 & 24519 \
\hline 11 \text { years } & 19287 & 24033 & 29947 & 37317 \
\hline 14 \text { years } & 24519 & 32442 & 42924 & 56795 \
\hline 17 \text { years } & 31170 & 43792 & 61525 & 86439 \
\hline
\end{array}$
E) $\begin{array} { | c | c | c | c | c | } 
\hline & \mathbf { 8 } \% & \mathbf { 1 0 } \% & \mathbf { 1 2 } \% & \mathbf { 1 4 } \% \
\hline 5 \text { years } & 62339 & 87583 & 123050 & 172878 \
\hline 8 \text { years } & 49038 & 64883 & 85849 & 113589 \
\hline 11 \text { years } & 38574 & 48067 & 59895 & 74633 \
\hline 14 \text { years } & 30344 & 35609 & 41787 & 49038 \
\hline 17 \text { years } & 23869 & 26380 & 29154 & 32220 \
\hline
\end{array}$

Quizplus · Accepted Answer

The correct values are calculated using the formula for continuous compounding interest, $A = P e^{rt}$, 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), and $t$ is the time the money is invested for in years. The values in option A are consistent with the results obtained from this formula when applied with the given interest rates and time periods, rounded to the nearest dollar.

Complete the Following Chart, Which Illustrates What Happens to $16,000