Question

Find the interest rate for a $5000 deposit accumulating to $7012.15, compounded quarterly for 8 years. The interest rate is % (Round to two decimal places as needed)

Answer 1

Answer: The interest rate is 5%

Solution:

Deposit: D=$5,000

Accumulating: A=$7012.15

Compounded quaterly→Number of periods per year: n=4

Number of years: y=8

A=D(1+r)^(ny)

$7012.15=$5,000(1+r)^(4*8)

$7012.15=$5,000(1+r)^32

Solving for r: Dividing both sides of the equation by $5,000:

$7012.15/$5,000=$5,000(1+r)^32/$5,000

1.40243=(1+r)^32

Raising both sides to the power 1/32:

1.40243^(1/32)=[(1+r)^32^(1/32)

1.0106250001=(1+r)^(32*1/32)

1.0106250001=(1+r)^(32/32)

1.0106250001=(1+r)^(1)

1.0106250001=1+r

Subtracting 1 both sides of the equation:

1.0106250001-1=1+r-1

0.0106250001=r

r=0.0106250001*100%

r=1.0625%

r=1.0625% quarterly

Annual interest rate: i=n*r

i=4*1.0625%

i=4.25%