Answer:
3.9%
Step-by-step explanation:
The formula for compound interest to apply is;
[tex]A=P(1+\frac{r}{n} )^{nt}[/tex]
where;
A=amount at the end
P=starting amount/principal
n=number of compounding years
t=total number of years
r=interest rate expressed as a decimal
Given
P=$4200, n=2, t=4 and A=$4900 R=?
Substitute values in equation, take r=r
[tex]A=P(1+\frac{r}{n} )^{nt} \\\\\\4900=4200(1+\frac{r}{2} )^{2*4} \\\\\\4900=4200(1+0.5r)^8[/tex]
Divide both sides by 4200
[tex]\frac{4900}{4200} =\frac{4200}{4200} (1+0.5r)^8\\\\\\1.1667=(1+0.5r)^8[/tex]
Introduce root 8 to the left hand side, thus eliminating the power 8 in the right hand side
[tex]\sqrt[8]{1.1667} =1+0.5r\\\\\\1.0195=1+0.5r\\\\\\1.0195-1=0.5r\\\\\\0.0195=0.5r\\\\\\\frac{0.0195}{0.5} =\frac{0.5r}{0.5} \\\\\\0.039=r[/tex]
r=3.9%
