8. suppose you invest in a cd account that accrues interest at an apr of 7.25% and compounds interest…

Explanation:

Step1: Identify the compound - interest formula

The compound - interest formula is $A = P(1+\frac{r}{n})^{nt}$, where $A$ is the final amount, $P$ is the principal (initial investment), $r$ is the annual percentage rate (APR) in decimal form, $n$ is the number of times interest is compounded per year, and $t$ is the number of years. We are given that $A=$10000$, $r = 0.0725$ (since $7.25%=0.0725$), $n = 52$ (compounded weekly), and $t = 5$. We need to solve for $P$.

Step2: Rearrange the formula for $P$

Starting with $A = P(1+\frac{r}{n})^{nt}$, we can solve for $P$ by dividing both sides of the equation by $(1+\frac{r}{n})^{nt}$. So, $P=\frac{A}{(1 +\frac{r}{n})^{nt}}$.

Step3: Substitute the given values into the formula for $P$

Substitute $A = 10000$, $r=0.0725$, $n = 52$, and $t = 5$ into the formula: [ \begin{align*} P&=\frac{10000}{(1+\frac{0.0725}{52})^{52\times5}}\ &=\frac{10000}{(1 + 0.00139423)^{260}}\ &=\frac{10000}{(1.00139423)^{260}} \end{align*} ] First, calculate $(1.00139423)^{260}\approx1.43777$. Then, $P=\frac{10000}{1.43777}\approx6955.28$.

Answer:

$6955.28$