Given:
Account 1 :
Principal amount = $ 4600
Interest = 2%
time = 4 years compounded monthly.
The future value is,
[tex]\begin{gathered} A_1=P(1+\frac{r}{n})^{nt} \\ A_1=4600(1+\frac{2}{100\times12})^{12\times4} \\ A_1=4600(1+0.001666667)^{48} \\ A_1=4982.79 \end{gathered}[/tex]Account 2:
Principal amount = $ 3000
Interest = 4%
time = 4 years compounded quarterly.
The future value is,
[tex]\begin{gathered} A_2=P(1+\frac{r}{n})^{nt} \\ A_2=3000(1+\frac{4}{100\times4})^{4\times4} \\ A_2=3000(1+0.01)^{16} \\ A_2=3517.74 \end{gathered}[/tex]The difference between the future values of both accounts is,
[tex]A_1-A_2=4982.79-3517.74=1465.05[/tex]Answer: Account 1 is better because the final value is $1465.05 more than the final value of Account 2 after four years.
