question: nicole invested $180 in an account paying an interest rate of 3.8% compounded quarterly. assuming…

Explanation:

Step1: Identify the compound - interest formula

The compound - interest formula is $A = P(1+\frac{r}{n})^{nt}$, where $A$ is the future value of the investment/loan, including interest, $P$ is the principal investment amount (the initial deposit or loan amount), $r$ is the annual interest rate (in decimal form), $n$ is the number of times that interest is compounded per year, and $t$ is the number of years the money is invested or borrowed for.

Step2: Convert the given values to the appropriate form

We are given that $P=$180$, $r = 3.8%=0.038$, $n = 4$ (compounded quarterly), and $t = 20$ years.

Step3: Substitute the values into the formula

$A=180(1 +\frac{0.038}{4})^{4\times20}$. First, calculate the value inside the parentheses: $\frac{0.038}{4}=0.0095$, and $1+\frac{0.038}{4}=1 + 0.0095=1.0095$. Then, calculate the exponent: $4\times20 = 80$. So, $A = 180\times(1.0095)^{80}$.

Step4: Calculate $(1.0095)^{80}$

Using a calculator, $(1.0095)^{80}\approx2.1079$.

Step5: Calculate the future value $A$

$A=180\times2.1079=$379.422\approx$379$

Answer:

$379$