In order to calculate the compound amount and the amount of interest earned, we can use the formula below:
[tex]A=P\cdot(1+\frac{i}{n})^{nt}[/tex]
Where A is the compound amount after t years, P is the principal (initial amount) i is the interest rate and n is how many times the interest is compounded in a year.
So, for P = 71000, i = 0.0102, t = 4 and n = 4, we have:
[tex]\begin{gathered} A=71000\cdot(1+\frac{0.0102}{4})^{4\cdot4}_{} \\ A=71000\cdot(1+0.00255)^{16} \\ A=73952.87 \end{gathered}[/tex]
Therefore the compound amount is $73952.87
The amount of interest is:
[tex]\begin{gathered} I=A-P \\ I=73952.87-71000 \\ I=2952.87 \end{gathered}[/tex]
So the amount of interest earned is $2952.87.
