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 interest will be earned over 2 years?
Answer
Explanation:
Step1: Identify 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), $n$ is the number of times compounded per year, and $t$ is the number of years. First, convert the rate to decimal: $r = 0.2%=0.002$, $P = 8000$, $n = 4$ (compounded quarterly), and $t = 2$.
Step2: Calculate the amount $A$
Substitute the values into the formula: $A=8000(1 +\frac{0.002}{4})^{4\times2}=8000(1 + 0.0005)^{8}$. First, calculate the value inside the parentheses: $1+0.0005 = 1.0005$. Then, $(1.0005)^{8}\approx1.004006$. So, $A = 8000\times1.004006=8032.048$.
Step3: Calculate the interest $I$
The interest $I$ is calculated by $I=A - P$. Substitute $A = 8032.048$ and $P = 8000$ into the formula: $I=8032.048 - 8000=32.048\approx32.05$.
Answer:
$32.05$