Answer:
[tex]\$2,369.11[/tex]
Step-by-step explanation:
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
Part 1)
[tex]t=2\ years\\ P=\$2,000\\ r=0.04\\n=12[/tex]
substitute in the formula above
[tex]A=2,000(1+\frac{0.04}{12})^{12*2}[/tex]
[tex]A=2,000(1.0033)^{24}[/tex]
[tex]A=\$2,166.29[/tex]
Part 2)
[tex]t=2\ years\\ P=\$2,166.29\\ r=0.045\\n=4[/tex]
substitute in the formula above
[tex]A=2,166.29(1+\frac{0.045}{4})^{4*2}[/tex]
[tex]A=2,166.29(1.01125)^{8}[/tex]
[tex]A=\$2,369.11[/tex]
