Question

Please Help! Algebra 2!

Answer 1

Answer:

The interest rate of the account is $3\%$

Step-by-step explanation:

we know that    

The compound interest formula is equal to  

$A=P(1+\frac{r}{n})^{nt}$  

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  

$t=14\ years\\ P=\ 1,863\\ A=\ 2,830.97\\n=4$  

substitute in the formula above  and solve for r

$\ 2,830.97=\ 1,863(1+\frac{r}{4})^{4*14}$  

$(2,830.97/1,863)=(1+\frac{r}{4})^{56}$  

$(2,830.97/1,863)^{1/56}=(1+\frac{r}{4})$

$[(2,830.97/1,863)^{1/56}-1]=\frac{r}{4}$    

$r=4*[(2,830.97/1,863)^{1/56}-1]\\ \\r= 0.03$

Convert to percent

$r= 0.03*100=3\%$