find how much interest $15,000 earns in 2 years in a certificate of deposit paying 4.5% interest compounded…

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. The interest earned $I=A - P$. First, convert the given values: $P = 15000$, $r=0.045$ (since $4.5%=0.045$), $n = 4$ (compounded quarterly), and $t = 2$.

Step2: Calculate the amount $A$

Substitute the values into the formula $A = P(1+\frac{r}{n})^{nt}$. $A=15000(1 +\frac{0.045}{4})^{4\times2}$ $A=15000(1 + 0.01125)^{8}$ $A=15000\times(1.01125)^{8}$ $(1.01125)^{8}\approx1.0938069$. So, $A = 15000\times1.0938069=16407.1035$.

Step3: Calculate the interest $I$

$I=A - P$. $I=16407.1035−15000 = 1407.1035$.

Answer:

$1407.10$