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

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%

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