[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
A=final amount
P=initial amount invested
r=rate in decimal form
n=number of times compounded per year
t=time in years
given
A=4900
P=4200
r=r (we are solving for this)
n=semianually=2 times per year
t=4
find r
[tex]4900=4200(1+\frac{r}{2})^{2*4}[/tex]
[tex]4900=4200(1+\frac{r}{2})^8[/tex]
divide both sides by 4200
[tex]\frac{4900}{4200}=(1+\frac{r}{2})^8[/tex]
take 8th root of both sides
[tex]\sqrt[8]{\frac{49}{42}}=1+\frac{r}{2}[/tex]
minus 1
[tex]-1+\sqrt[8]{\frac{49}{42}}=\frac{r}{2}[/tex]
multiply both sides by 2
[tex]-2+2\sqrt[8]{\frac{49}{42}}=r[/tex]
r=0.038911
r=3.891% so about 3.89%
