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=t\ years\\ P=\$10,000\\ r=0.12\\n=4[/tex]
substitute in the formula above
[tex]A=10,000(1+\frac{0.12}{4})^{4t}[/tex]
[tex]A=10,000(1+0.03)^{4t}[/tex]
[tex]A=10,000(1.03)^{4t}[/tex]
therefore
the answer is
[tex]A=10,000(1.03)^{4t}[/tex]
