Respuesta :
The question gives us the following information:
Principal = $8,000
Time = 1 year
Interest rate = 4.25%, compounded quarterly.
We're going to use the following formula to solve the questions:
[tex]A=P(1+\frac{r}{n})^{n(t)}[/tex]Where A is the total amount at the end of the investment, r is the annual interest rate, n is the number of compounding periods in a year, and t is the time in number of years.
By substituting the given, we get:
[tex]\begin{gathered} A=8,000(1+\frac{0.4025}{4})^{4(1)} \\ \\ A=8,000(1.010625)^4 \\ \\ A=8,345.4572 \end{gathered}[/tex]Therefore, the amount is $8,345.46.
Interest earned is the additional money received from the investment. So we simply subtract the principal from the total amount.
[tex]\begin{gathered} Interest=8,345.46-8,000 \\ \\ Interest=345.46 \end{gathered}[/tex]So interest is $345.46.
Lastly, to find the annual percentage yield, we divide the interest earned by the principal amount invested.
[tex]\begin{gathered} Yield=\frac{345.46}{8,000} \\ \\ Yield=0.0431821 \end{gathered}[/tex]The yield is 0.043182 or 4.318%.
