dom has a savings account that earns 5.5% interest compounded daily. on may 5, the amount in the account was…

Explanation:

Step1: Identify the compound - interest formula

The compound - interest formula for daily compounding 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. Here, $P=$28214.35$, $r = 0.055$ (since $5.5%=0.055$), $n = 365$ (compounded daily), and $t=\frac{90}{365}$ years.

Step2: Calculate the amount $A$ after 90 days

$A=28214.35(1 +\frac{0.055}{365})^{365\times\frac{90}{365}}=28214.35(1+\frac{0.055}{365})^{90}$. First, calculate $\frac{0.055}{365}\approx0.000150685$. Then $1+\frac{0.055}{365}=1.000150685$. $(1.000150685)^{90}\approx1.013617$. So, $A = 28214.35\times1.013617\approx28601.97$.

Step3: Calculate the interest earned

The interest earned $I=A - P$. $I=28601.97 - 28214.35=$387.62$.

Answer:

$387.62$