Answer:
Option B) $5,612.16
Step-by-step explanation:
Part 1) Account I earns 4% annual simple interest.
we know that
The simple interest formula is equal to
[tex]A=P(1+rt)[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest
t is Number of Time Periods
in this problem we have
[tex]t=3\ years\\ P=\$2,500\\r=4\%=4/100=0.04[/tex]
substitute in the formula above
[tex]A=2,500(1+0.04*3)[/tex]
[tex]A=2,500(1.12)[/tex]
[tex]A=\$2,800[/tex]
Part 2) Account II earns 4% interest compounded annually.
we know that
The compound interest formula is equal to
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
[tex]t=3\ years\\ P=\$2,500\\r=4\%=4/100=0.04\\n=1[/tex]
substitute in the formula above
[tex]A=2,500*(1+\frac{0.04}{1})^{3}[/tex]
[tex]A=2,500*(1.04)^{3}[/tex]
[tex]A=\$2,812.16[/tex]
Part 3) What is the sum of the balances of Account I and Account II at the end of 3 years?
Sum the two final investment
[tex]\$2,800+\$2,812.16=\$5.612.16[/tex]
