Answer:
$259
Step-by-step explanation:
\text{Rate 1: }5\tfrac{1}{2}\%=5+1/2=
Rate 1: 5
2
1
%=5+1/2=
\,\,5.5\%\rightarrow 0.055
5.5%→0.055
\text{Rate 2: }5\tfrac{3}{4}\%=5+3/4=
Rate 2: 5
4
3
%=5+3/4=
\,\,5.75\%\rightarrow 0.0575
5.75%→0.0575
\text{Calculate Final Amount for Kylie}
Calculate Final Amount for Kylie
\overline{\phantom{\text{Calculate Final Amount for Kylie}}}
Calculate Final Amount for Kylie
\text{Compounded Annually:}
Compounded Annually:
A=P(1+r)^t
A=P(1+r)
t
P=2800\hspace{35px}r=0.055\hspace{35px}t=12
P=2800r=0.055t=12
Given values
A=2800(1+0.055)^{12}
A=2800(1+0.055)
12
Plug in values
A=2800(1.055)^{12}
A=2800(1.055)
12
Add
A=5323.381
A=5323.381
Use calculator
\text{Calculate Final Amount for Ariana}
Calculate Final Amount for Ariana
\overline{\phantom{\text{Calculate Final Amount for Ariana}}}
Calculate Final Amount for Ariana
\text{Compounded Continuously:}
Compounded Continuously:
A=Pe^{rt}
A=Pe
rt
P=2800\hspace{35px}r=0.0575\hspace{35px}t=12
P=2800r=0.0575t=12
Given values
A=2800e^{0.0575(12)}
A=2800e
0.0575(12)
Plug in
A=2800e^{0.69}
A=2800e
0.69
Multiply
A=5582.4035
A=5582.4035
Use calculator (with e button)
\text{How much more money Ariana has:}
How much more money Ariana has:
5582.4035-5323.381
5582.4035−5323.381
259.0225
259.0225
