Answer:
[tex]\$164.62[/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
case A) compounded monthly
in this problem we have
[tex]t=25\ years\\ P=\$5,000\\ r=0.06\\n=12[/tex]
substitute in the formula above
[tex]A=\$5,000(1+\frac{0.06}{12})^{12*25}=\$22,324.85[/tex]
case B) compounded quarterly
in this problem we have
[tex]t=25\ years\\ P=\$5,000\\ r=0.06\\n=4[/tex]
substitute in the formula above
[tex]A=\$5,000(1+\frac{0.06}{4})^{4*25}=\$22,160.23[/tex]
Find the difference
[tex]\$22,324.85-\$22,160.23=\$164.62[/tex]
