Answer:
The interest rate of the account is [tex]3\%[/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=14\ years\\ P=\$1,863\\ A=\$2,830.97\\n=4[/tex]
substitute in the formula above and solve for r
[tex]\$2,830.97=\$1,863(1+\frac{r}{4})^{4*14}[/tex]
[tex](2,830.97/1,863)=(1+\frac{r}{4})^{56}[/tex]
[tex](2,830.97/1,863)^{1/56}=(1+\frac{r}{4})[/tex]
[tex][(2,830.97/1,863)^{1/56}-1]=\frac{r}{4}[/tex]
[tex]r=4*[(2,830.97/1,863)^{1/56}-1]\\ \\r= 0.03[/tex]
Convert to percent
[tex]r= 0.03*100=3\%[/tex]
