test yourself! practice tool\narchie invests $27,000 into a savings account with an interest rate of 2.25%…

Answer:

$32419.47$

Explanation:

Step1: Identify the compound - interest formula

$A = P(1+\frac{r}{n})^{nt}$ where $A$ is the amount of money accumulated after $n$ years, including interest, $P$ is the principal amount (the initial amount of money), $r$ is the annual interest rate (in decimal form), $n$ is the number of times that interest is compounded per year, and $t$ is the time the money is invested for in years.

Step2: Convert the given values to the correct form

$P=$27000$, $r = 2.25%=0.0225$, $n = 12$ (compounded monthly), and $t = 8$ years.

Step3: Substitute the values into the formula

$A=27000(1 +\frac{0.0225}{12})^{12\times8}$

Step4: Calculate the value inside the parentheses

$\frac{0.0225}{12}=0.001875$, then $1+\frac{0.0225}{12}=1 + 0.001875=1.001875$

Step5: Calculate the exponent

$12\times8 = 96$

Step6: Calculate $(1.001875)^{96}$

Using a calculator, $(1.001875)^{96}\approx1.197017$

Step7: Calculate the final amount $A$

$A = 27000\times1.197017\approx32419.47$