Hello!
Let's solve alternative (a):
For simple interest, we'll use the formula below:
[tex]A=P(1+\frac{r}{100}\cdot t)[/tex]Let's replace them with the values:
[tex]\begin{gathered} A=14,000(1+0.07\cdot15) \\ A=14,000(1+1.05) \\ A=14,000\cdot2.05 \\ A=\$28,700 \end{gathered}[/tex]Solving alternative (b):
To compound interest, we'll modify the formula:
[tex]A=P(1+\frac{r}{100})^t[/tex]So, we'll have:
[tex]\begin{gathered} A=14,000(1+0.07)^{15} \\ A=14,000(1.07)^{15} \\ A=14,000\cdot2.75903 \\ A=\$\text{ }38,626.42 \end{gathered}[/tex]Solving alternative (c):
[tex]\begin{gathered} A=P(1+\frac{r}{4})^{4t} \\ A=14,000(1+\frac{0.07}{4})^{4\cdot15} \\ A=14,000(1.0175)^{60} \\ A\cong$ \$\text{ }39,645.43 $ \end{gathered}[/tex]Solving alternative (d):
[tex]\begin{gathered} A=P(1+\frac{r}{12})^{12\cdot t} \\ A=14,000(1+\frac{0.07}{12})^{12\cdot15} \\ A\cong\$\text{ }$ 39,885.25 $ \end{gathered}[/tex]