Answer:
[tex]r=6.5\%[/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=4\ years\\ P=\$8,000\\A=\$10,292.76\\r=?\\n=1[/tex]
substitute in the formula above
[tex]10,292.76=8,000(1+\frac{r}{1})^{1*4}[/tex]
solve for r
[tex]10,292.76=8,000(1+r)^{4}[/tex]
[tex](10,292.76/8,000)=(1+r)^{4}[/tex]
Elevated to 1/4 both sides to remove the exponent in the right side
[tex](10,292.76/8,000)^{1/4}=(1+r)[/tex]
[tex]r=(10,292.76/8,000)^{1/4}-1[/tex]
[tex]r=0.065[/tex]
Convert to percentage
[tex]r=6.5\%[/tex]
