It is given that principal is 250 dollar at 6 percent compounded.
a. Annually.
Use n=1
Use the formula for amount.
[tex]A=P(1+\frac{r}{n})^{nt}_{}[/tex]
Substitute the values.
[tex]A=250(1+\frac{6}{100})^8=250(1.06)^8[/tex][tex]A=398.46dollar[/tex]
For the interest , A=P+I.
Substitute the values,
[tex]398.46=250+I[/tex][tex]I=398.46-250=148.46dollar.[/tex]
B. Quarterly.
Use n =4
Use the formula for amount.
[tex]A=P(1+\frac{r}{n})^{nt}[/tex][tex]A=250(1+\frac{6}{100\times4})^{4\times8}=250(1+0.015)^{32}[/tex][tex]A=402.58dollar.[/tex]
The interest is determined as A=P+I.
[tex]I=402.58-250=152.58\text{ dollar}[/tex]
C. Monthly.
Use n =12
Use the amount formula.
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
Substitute the values.
[tex]A=250(1+\frac{6}{100\times12})^{12\times8}[/tex][tex]A=250(1+0.005)^{96}=403.54dollar[/tex]
Hence the amount is 403.54 dollar.
For interest , A=P+I
Substitute the values and find I,
[tex]403.54-250=I[/tex][tex]I=153.54dollar.[/tex]
Hence the interest earned is 153.54 dollar.
