Respuesta :
.Explanation.
To determine the best account to choose, we will have to check for the amount each account will yield
For the first account, with 2.5% simple interest annually
To find how much this account will yield at 2.5% simple interest annually, we will use the formula
[tex]A=P+\frac{P\times R\times T}{100}[/tex]Where
[tex]\begin{gathered} p=\text{ \$1500} \\ r=2.5\text{ \%} \\ t=18-15=3years \end{gathered}[/tex]Thus, the first account will yield
[tex]\begin{gathered} A=1500+\frac{1500\times2.5\times3}{100} \\ \\ A=1500+15\times7.5 \\ A=1500+112.5 \\ A=\text{ \$1612.5} \end{gathered}[/tex]For the second account with 2% interest compounded annually
[tex]\begin{gathered} A=P(1+\frac{r}{100})^t \\ where \\ P=1500 \\ r=2\text{ \%} \\ t=3 \end{gathered}[/tex]Thus the account will yield
[tex]\begin{gathered} A=1500(1+\frac{2}{100})^3 \\ A=1500(1.0612) \\ A=\text{ \$}1591.81 \end{gathered}[/tex]We can see that the first account with 2.5% simple interest annually yields $1612.50 and
The second account with 2% interest compounded annually yields $1591.81
The difference in the accounts will be
[tex]\text{ \$}1612.50-\text{ \$}1591.81=\text{ \$20.69}[/tex]Thus, I will choose the first account with 2.5% simple interest annually, because it yields $20.69 more than the second account after 3 years
