Answer:
[tex]5.24\%[/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
in this problem we have
[tex]t=20\ years\\ P=\$770\\A=\$2,180\\n=4[/tex]
substitute in the formula above
[tex]2,180=770(1+\frac{r}{4})^{4*20}[/tex]
[tex](2,180/770)=(1+\frac{r}{4})^{80}[/tex]
Elevated both sides to 1/80
[tex](2,180/770)^{\frac{1}{80}}=(1+\frac{r}{4})[/tex]
[tex]\frac{r}{4}=(2,180/770)^{\frac{1}{80}}-1[/tex]
[tex]r=0.0524[/tex]
convert to percent
[tex]0.0524*100=5.24\%[/tex]
