find the compound interest and future value. round your answers to the nearest cent. do not round. principal…

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, $P$ 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 compound interest $I=A - P$. Given $P = 1485$, $r=0.004$ (since $0.4%=0.004$), $n = 2$ (compounded semi - annually), and $t = 1.5$ years.

Step2: Calculate the future value $A$

Substitute the values into the formula: [ \begin{align*} A&=1485\times(1 +\frac{0.004}{2})^{2\times1.5}\ &=1485\times(1+0.002)^{3}\ &=1485\times(1.002)^{3}\ &=1485\times1.006012008\ &=1493.928832 \end{align*} ] Rounding to the nearest cent, $A\approx1493.93$.

Step3: Calculate the compound interest $I$

$I=A - P$. $I = 1493.93-1485=8.93$

Answer:

The future value is $$1493.93$, and the compound interest is $$8.93$.