$1,500 is invested in an account with a 3% in...
$1,500 is invested in an account with a 3% interest rate that is compounded quarterly. how much money is in the account at the end of one year? $? round to the nearest cent.
Answer
# Answer:
$1545.68$
# Explanation:
## Step1: Identify compound - interest formula
$A = P(1+\frac{r}{n})^{nt}$
## Step2: Define the variables
$P = 1500$, $r=0.03$, $n = 4$, $t = 1$
## Step3: Substitute values into formula
$A=1500(1 +\frac{0.03}{4})^{4\times1}$
## Step4: Calculate inside the parentheses
$1+\frac{0.03}{4}=1 + 0.0075=1.0075$
## Step5: Calculate the exponent
$(1.0075)^{4}=1.030339$
## Step6: Multiply by the principal
$A = 1500\times1.030339=1545.5085\approx1545.68$