ANSWER :
a. $5801.11
b. $801.11
EXPLANATION :
Recall the compound interest formula :
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
where A = Future amount
P = Principal amount
r = rate of interest
n = number of compounding in a year
t = time in years
From the problem, the principal amount is P = $5000
the rate of interest is r = 7.5% or 0.075
n = 4 times in a year
t = 2 years
Using the formula above :
[tex]\begin{gathered} A=5000(1+\frac{0.075}{4})^{4(2)} \\ \\ A=5801.11 \end{gathered}[/tex]
a. The balance at the end of the investment period is $5801.11
b. The interest earned is the difference between the future amount and the principal amount.
That will be :
[tex]5801.11-5000=801.11[/tex]
