use the information in the table to answer the following questions.\n|principal|rate|compounded|time|\n|$8000…
use the information in the table to answer the following questions.\n|principal|rate|compounded|time|\n|$8000|0.2%|quarterly|2 years|\nhow much money will be in the account after 2 years?
Answer
Explanation:
Step1: Identify the 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.
Step2: Convert the given values to the correct form
The principal $P=$8000$, the annual interest rate $r = 0.2%=0.002$, the number of times compounded per year $n = 4$ (since it's compounded quarterly), and the number of years $t = 2$.
Step3: Substitute the values into the formula
$A=8000(1 +\frac{0.002}{4})^{4\times2}$. First, calculate the value inside the parentheses: $\frac{0.002}{4}=0.0005$, and $1 + 0.0005=1.0005$. Then, calculate the exponent: $4\times2 = 8$. So, $A = 8000\times(1.0005)^{8}$.
Step4: Calculate $(1.0005)^{8}$
Using a calculator, $(1.0005)^{8}\approx1.004006$.
Step5: Calculate the final amount $A$
$A=8000\times1.004006=$8032.05$
Answer:
$$8032.05$