$5,200 is invested in an account with a 4.1% ...
$5,200 is invested in an account with a 4.1% 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:
$5413.97$
# Explanation:
## Step1: Identify compound - interest formula
$A = P(1+\frac{r}{n})^{nt}$
## Step2: Define variables
$P = 5200$, $r=0.041$, $n = 4$, $t = 1$
## Step3: Substitute values into formula
$A=5200(1 +\frac{0.041}{4})^{4\times1}$
$A=5200(1 + 0.01025)^{4}$
$A=5200\times(1.01025)^{4}$
## Step4: Calculate $(1.01025)^{4}$
$(1.01025)^{4}=1.041147$
## Step5: Calculate $A$
$A = 5200\times1.041147=5413.9644\approx5413.97$