$1,600 is invested in an account with a 2.4% ...
$1,600 is invested in an account with a 2.4% 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:
$1638.78$
# Explanation:
## Step1: Identify compound - interest formula
$A = P(1+\frac{r}{n})^{nt}$
## Step2: Define variables
$P = 1600$, $r=0.024$, $n = 4$, $t = 1$
## Step3: Substitute values into formula
$A=1600(1 +\frac{0.024}{4})^{4\times1}$
## Step4: Calculate inside the parentheses
$1+\frac{0.024}{4}=1 + 0.006=1.006$
## Step5: Calculate the exponent part
$(1.006)^{4}=1.006\times1.006\times1.006\times1.006\approx1.024147$
## Step6: Calculate the final amount
$A = 1600\times1.024147\approx1638.6352\approx1638.78$