Given:
The interest amount earned is, P = $735.
The number of years is, n = 7.
The rate of interest is, r = 5.75% = 0.0575.
The objective is to find the amount of interest earned.
Explanation:
The general formula to find the total amount earned by compount interest is,
[tex]A=P(1+\frac{r}{n})^{n(t)}[/tex]Here, n represents the number of times the interest is compounded per year. It is given that the interest is compounded semi-annually.
So, the value of n = 2.
To find total amount:
Now, substitute the given values in the general formula.
[tex]\begin{gathered} A=735(1+\frac{0.0575}{2})^{2(7)} \\ =735(1+0.02875)^{14} \\ =1093.01 \end{gathered}[/tex]To find interest amount:
Now, the interest amount can be calculated as,
[tex]\begin{gathered} CI=A-P \\ =1093.01-735 \\ =358.01 \end{gathered}[/tex]Hence, the interest earned is $358.01.
