linda invested $4500 in an account that pays an annual interest rate of 3.2%, compounded quarterly. answer…

Explanation:

Step1: Identify compound - interest formula

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.

Step2: Convert given values

Given $P = 4500$, $r=0.032$ (since $3.2%=0.032$), $n = 4$ (compounded quarterly), and $t = 1$.

Step3: Calculate the amount after one year

Substitute the values into the formula: $A=4500(1 +\frac{0.032}{4})^{4\times1}=4500(1 + 0.008)^{4}=4500\times(1.008)^{4}$. $(1.008)^{4}=1.008\times1.008\times1.008\times1.008=1.0324897792$. $A = 4500\times1.0324897792=4646.2040064\approx4646.20$.

Step4: Calculate the effective - annual - interest rate formula

The formula for the effective - annual - interest rate $r_{eff}$ is $r_{eff}=(1+\frac{r}{n})^{n}-1$.

Step5: Substitute values for effective - annual - interest rate

Substitute $r = 0.032$ and $n = 4$ into the formula: $r_{eff}=(1+\frac{0.032}{4})^{4}-1=(1 + 0.008)^{4}-1$. We already know $(1.008)^{4}=1.0324897792$. $r_{eff}=1.0324897792-1=0.0324897792$. Convert to percentage: $r_{eff}=3.25%$ (rounded to the nearest hundredth of a percent).

Answer:

(a) $$4646.20$ (b) $3.25%$