Respuesta :
The amount A earned at the end of a given period t for an interest compounded annually is expressed as
[tex]\begin{gathered} A\text{ = P(}1+\frac{r}{n})^{nt} \\ \text{where} \\ A=\text{Amount} \\ P\text{ = principal (amount deposited)} \\ r=interest\text{ } \\ n\text{ = }number\text{ of times interest applied per time period} \\ t\text{ = period elapsed} \end{gathered}[/tex]Account 1:
Amount deposited = 10000. thus, P = 10000
r = 4% = 0.04
Since the interest is compounded annually, n= 1
t = 3.
Thus, the amount in account 1 after 3 years is evaluated as
[tex]\begin{gathered} A\text{ = P(}1+\frac{r}{n})^{nt} \\ A\text{ = 10000(1+}\frac{0.04}{1})^{(1\times3)} \\ =10000(1+0.04)^3\text{ } \\ =10000(1.04)^3 \\ \Rightarrow A\text{ = }11248.64 \end{gathered}[/tex]The amount earned at the end of 3 years in account 1 is $ 11248.64
Account 2:
P =10000
r = 3% = 0.03
n =1
t = 3
Thus, the amount in account 2 after 3 years is evaluated as
[tex]\begin{gathered} A\text{ = P(}1+\frac{r}{n})^{nt} \\ =10000(1+\frac{0.03}{1})^{(1\times3)} \\ =10000(1+0.03)^3 \\ =10000(1.03)^3 \\ \Rightarrow A=10927.27 \end{gathered}[/tex]The amount earned at the end of 3 years in account 2 is $ 10927.27
How much more will be in account 1 than account 2:
[tex]\begin{gathered} Amount\text{ earned in account 1 - amount earned in account 2} \\ $11248.64$\text{ - }$10927.27$ \\ =\text{ 321.3}7 \\ \end{gathered}[/tex]Hence, there will be $ 321.37 in account 1 than account 2.
