Given,
The principal amount is $16000.
The time period is 5 years.
a)The rate of interest is 5%.
The amount compounded quarterly is,
[tex]\begin{gathered} \text{Amount}=\text{ principal}\times(1+\frac{r}{100})^t \\ =16000(1+\frac{5}{4\times100})^{5\times4} \\ =16000\times(1+0.0125)^{20} \\ =16000\times(1.0125)^{20} \\ =20512.60 \end{gathered}[/tex]Hence, the amount compounded quarterly is $20512.60.
b)The rate of interest is 5%.
The amount compounded monthly is,
[tex]\begin{gathered} \text{Amount}=\text{ principal}\times(1+\frac{r}{100})^t \\ =16000(1+\frac{5}{12\times100})^{5\times12} \\ =16000\times(1+0.004167)^{60} \\ =16000\times(1.004167)^{60} \\ =20533.74 \end{gathered}[/tex]Hence, the amount compounded monthy is $20533.74.
c)The rate of interest is 3%.
The amount compounded quarterly is,
[tex]\begin{gathered} \text{Amount}=\text{ principal}\times(1+\frac{r}{100})^t \\ =16000(1+\frac{3}{4\times100})^{5\times4} \\ =16000\times(1+0.0075)^{20} \\ =16000\times(1.0075)^{20} \\ =18,578.95 \end{gathered}[/tex]Hence, the amount compounded quarterly is $18578.95.
d)The rate of interest is 3%.
The amount compounded monthly is,
[tex]\begin{gathered} \text{Amount}=\text{ principal}\times(1+\frac{r}{100})^t \\ =16000(1+\frac{3}{12\times100})^{5\times12} \\ =16000\times(1+0.0025)^{60} \\ =16000\times(1.0025)^{60} \\ =18585.87 \end{gathered}[/tex]Hence, the amount compounded monthy is $18,585.87.