We have the following data for an investment:
• A0 = initial amount of money ($) invested = 1500.00,
,• r = interest rate in decimal = 3%/100% = 0.03,
,• the interest is compounded quarterly.
Q) We want to know how much money will be in the account at the end of one year.
A) To calculate the amount of money after n years with an interest rate in decimal r, we can use the following formula:
[tex]A(n)=A_0\cdot(1+\frac{r}{4})^{4n}[/tex]Because we want to know the amount of money after one year, we must use n = 1. Replacing the data of our problem in the equation above we get:
[tex]\begin{gathered} A(1)=1500\cdot(1+\frac{0.03}{4})^{4\cdot1} \\ A(1)=1500\cdot(1.0075)^4 \\ A(1)\cong1545.51 \end{gathered}[/tex]Answer
A. $1,545.51
