an author receives a $7,600 advance payment for a book publishing deal and wants to place the money in a…

Explanation:

Step1: Calculate semi - annually compounded amount

The compound - interest formula is $A = P(1+\frac{r}{n})^{nt}$, where $P=$7000$, $r = 0.0338$, $n = 2$ (semi - annual compounding), and $t = 8$ years. $A_{1}=7000(1 +\frac{0.0338}{2})^{2\times8}=7000(1 + 0.0169)^{16}=7000\times1.0169^{16}$. $1.0169^{16}\approx1.285793$, so $A_{1}=7000\times1.285793=$9000.551$.

Step2: Calculate continuously compounded amount

The continuous - compounding formula is $A = Pe^{rt}$, where $P = 7000$, $r=0.0328$, and $t = 8$. $A_{2}=7000\times e^{0.0328\times8}=7000\times e^{0.2624}$. Since $e^{0.2624}\approx1.299604$, then $A_{2}=7000\times1.299604=$9097.228$.

Answer:

The continuously compounded account will have a larger balance of $$9097.23$ (rounded to the nearest cent). Since the closest option to our calculated value for the continuously compounded account is "The continuously compounded account will have a larger balance of $$9,937.23$" is incorrect based on our calculations, and re - calculating with more precision: $A_{1}=7000(1+\frac{0.0338}{2})^{16}=7000\times(1.0169)^{16}\approx7000\times1.2857934=$9000.5538$ $A_{2}=7000\times e^{0.0328\times8}=7000\times e^{0.2624}\approx7000\times1.2996041=$9097.2287$. The continuously compounded account will have a larger balance. None of the provided options are correct based on accurate calculations. But if we assume some rounding differences in the provided options, the closest conceptually is "The continuously compounded account will have a larger balance of $$9,937.23$" (although the value is off). If we had to choose from the given options, we note that the continuously compounded account should have a larger balance, and the closest option indicating that is: The continuously compounded account will have a larger balance of $$9,937.23$ (even though the actual calculated value is different).