Answer: The interest rate is 5%
Solution:
Deposit: D=$9,000
Accumulating: A=$14,075.49
Compounded quaterly→Number of periods per year: n=4
Number of years: y=9
A=D(1+r)^(ny)
$14,075.49=$9,000(1+r)^(4*9)
$14,075.49=$9,000(1+r)^36
Solving for r: Dividing both sides of the equation by $9,000:
$14,075.49/$9,000=$9,000(1+r)^36/$9,000
1.563943333=(1+r)^36
Raising both sides to the power 1/36:
1.563943333^(1/36)=[(1+r)^36]^(1/36)
1.012499991=(1+r)^(36*1/36)
1.012499991=(1+r)^(36/36)
1.012499991=(1+r)^(1)
1.012499991=1+r
Subtracting 1 both sides of the equation:
1.012499991-1=1+r-1
0.012499991=r
r=0.012499991
r=0.012499991*100%
r=1.2499991%
r=1.25% quarterly
Annual interest rate: i=n*r
i=4*1.25%
i=5%