$5,200 is invested in an account with a 4.1% interest rate that is compounded quarterly. how much money is…

$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.

$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 $A$

$A = 5200\times1.041147=5413.9644\approx5413.97$