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 correctly follow this formula when applied to the given interest rates and time periods.

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