Answer
a) $5026.16$
b) $5634.1$
c) $6315.58$
Work Step by Step
In $A(t)=P(1+\frac{r}{n})^{nt}$ for compound interest $P,r,n,t$ respectively stand for the principal, interest rate per year, the number of times the interest is compounded per year and the number of years. $A(t)$ is the amount after $t$ years. So if we invest $P=4000$ at an interest rate of $r=0.0575$ compounded quarterly ($n=4$), the amount after $t$ years is:
a) $A(4)=4000(1+\frac{0.0575}{4})^{4(4)}\approx5026.16$
b) $A(6)=4000(1+\frac{0.0575}{4})^{4(6)}\approx5634.1$
c) $A(8)=4000(1+\frac{0.0575}{4})^{4(8)}\approx6315.58$
