juan invests $3,000 in a cd that yields 3.4% compounded daily for 5 years. how much is his cd worth after 5…

Explanation:

Step1: Identify the compound - interest formula

The compound - interest formula when compounded $n$ times a year 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 compounded per year, $t$ is the number of years, and $A$ is the amount of money accumulated after $n$ years, including interest. Here, $P=$3000$, $r = 0.034$ (since $3.4%=0.034$), $n = 365$ (compounded daily), and $t = 5$ years.

Step2: Substitute the values into the formula

$A=3000(1 +\frac{0.034}{365})^{365\times5}$ First, calculate the value inside the parentheses: $\frac{0.034}{365}\approx0.00009315$. Then $1+\frac{0.034}{365}=1 + 0.00009315=1.00009315$. Next, calculate the exponent: $365\times5 = 1825$. So, $A = 3000\times(1.00009315)^{1825}$.

Step3: Calculate $(1.00009315)^{1825}$

Using a calculator, $(1.00009315)^{1825}\approx1.180947$.

Step4: Calculate the final amount $A$

$A=3000\times1.180947=$3542.841$. Rounding to the nearest cent, $A\approx$3542.84$.

Answer:

$3542.84$