To answer this question, we will use the following formula for simple interest:
[tex]F=A(1+rt),[/tex]
and the following formula for annually compounded interest:
[tex]F=A(1+r)^t,[/tex]
where t is the time in years, A is the initial amount, and r is the rate of interest as a decimal.
Substituting A=1600/2=800, r= 0.06, and t=5 in the formula for simple interest, we get:
[tex]F=800(1+0.06\times5)\text{.}[/tex]
Simplifying the above result, we get.
[tex]F=1040.[/tex]
Therefore, after 5 years, she earned:
[tex]1040-800=240.[/tex]
Substituting A=1600/2=800, r= 0.05, and t=5 in the formula for compounded interest, we get:
[tex]F=800(1+0.05)^5.[/tex]
Simplifying the above result, we get:
[tex]F=1021.03.[/tex]
Therefore, after 5 years she will have earned:
[tex]1021.03-800=221.03.[/tex]
Therefore, after 5 years she will have a total of:
[tex]461.03.[/tex]
dollars.
Answer: $461.03.
