1. you have the choice of investing $5,000 in one of two investments. the first option earns you 4.25%…

Explanation:

Step1: Calculate simple - interest amount

The simple - interest formula is $A = P(1+rt)$, where $P$ is the principal amount, $r$ is the annual interest rate (in decimal form), and $t$ is the time in years. Given $P=$5000$, $r = 0.0425$, and $t = 10$. $A_1=5000(1 + 0.0425\times10)$

Step2: Simplify the simple - interest formula

$A_1=5000(1+0.425)$ $A_1=5000\times1.425$ $A_1 = 7125$

Step3: Calculate compound - interest amount

The compound - interest formula is $A=P(1+\frac{r}{n})^{nt}$, where $P$ is the principal amount, $r$ is the annual interest rate (in decimal form), $n$ is the number of times interest is compounded per year, and $t$ is the number of years. Given $P = 5000$, $r=0.0405$, $n = 12$ (compounded monthly), and $t = 10$. $A_2=5000(1+\frac{0.0405}{12})^{12\times10}$

Step4: Simplify the compound - interest formula

First, calculate the value inside the parentheses: $\frac{0.0405}{12}=0.003375$. Then $1+\frac{0.0405}{12}=1.003375$. And $12\times10 = 120$. $A_2=5000\times(1.003375)^{120}$ Using a calculator, $(1.003375)^{120}\approx1.49083$. $A_2=5000\times1.49083=$7454.15$

Answer:

The simple - interest investment is worth $$7125$ and the compound - interest investment is worth $$7454.15$.