Respuesta :
In the case of the simple annual interest we can calculate what we earn by applying a rule of three. In that case
[tex]\begin{gathered} 50000\rightarrow100 \\ x\rightarrow3.15 \end{gathered}[/tex]Then the anual interest is
[tex]\begin{gathered} x=\frac{(3.15)(50000)}{100} \\ =\frac{157500}{100} \\ =1575 \end{gathered}[/tex]Therefore the simple interest earned in one year is $1575.00.
To calculate the compound interest we have to use the following formula
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Where
[tex]\begin{gathered} A\text{ }the\text{ future value including interest} \\ P\text{ }the\text{ initial deposit} \\ r\text{ the annual interest rate in decimal } \\ n\text{ number }of\text{ times that interest is compound } \\ t\text{ }the\text{ time money is invested } \end{gathered}[/tex]In this case we have
[tex]\begin{gathered} P=50000 \\ r=.0315 \\ n=52\text{ (since the year has 52 WEEks)} \\ t=1\text{ (since we want to know what happens after a year)} \end{gathered}[/tex]Then we have
[tex]\begin{gathered} A=50000(1+.\frac{0315}{52})^{(52)(1)} \\ =51599.57 \end{gathered}[/tex]To know the annual interest earned in the second case we have to substract de initial deposit to A, then the annual compound interest we earned is $1599.57.
Finally to know how much interest we earned in the second case we substract $1575.00 to $1599.57.
Then we earned $24.57 more if we compound weekly.
