$1,600 is invested in an account with a 2.4% interest rate that is compounded quarterly. how much money is…

$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.

$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

$A = 1600\times1.024147\approx1638.6352\approx1638.78$