find the interest rate for a $9000 deposit accumulating to $14,075.49, compounded quarterly for 9 years

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%