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

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 compounded per year, and $t$ is the number of years. $P = 1425$, $r=0.005$ (since $0.5%=0.005$), $n = 2$ (compounded semiannually), and $t = 13$.

Step2: Calculate the exponent

First, calculate $nt$: $nt=2\times13 = 26$.

Step3: Calculate the value inside the parentheses

Next, calculate $1+\frac{r}{n}$: $1+\frac{0.005}{2}=1 + 0.0025=1.0025$.

Step4: Calculate the future value $A$

Then, calculate $(1+\frac{r}{n})^{nt}=(1.0025)^{26}$. Using a calculator, $(1.0025)^{26}\approx1.06777$. $A = P(1+\frac{r}{n})^{nt}=1425\times1.06777\approx1521.57$.

Step5: Calculate the compound interest

The compound interest $CI=A - P$. $CI=1521.57-1425 = 96.57$.

Answer:

The future value is $$1521.57$, and the compound interest is $$96.57$.