SOLUTION: If an investment of $2000 grows to $2633.62 in eight years with interest compounded annually, what is the interest rate? (Round your answer to one decimal place.)

Algebra ->  Test -> SOLUTION: If an investment of $2000 grows to $2633.62 in eight years with interest compounded annually, what is the interest rate? (Round your answer to one decimal place.)      Log On


   

Question 1058424: If an investment of $2000 grows to $2633.62 in eight years with interest compounded annually, what is the interest rate? (Round your answer to one decimal place.)
Answer by solve_for_x(190) About Me  (Show Source):
You can put this solution on YOUR website!
Use the equation:

FV+=+PV%281+%2B+r%2Fn%29%5E%28nt%29

where FV is the future value, PV is the present value, r is the annual interest rate,
n is the number of periods per year, and t is the number of years.

For this problem, FV = 2633.62, PV = 2000, n = 1, and t = 8, which gives:

2633.62+=+2000%281+%2B+r%29%5E8

Solving for r gives:

%281+%2B+r%29%5E8+=+2633.62+%2F+2000

8%2Aln%281+%2B+r%29+=+ln%282633.62%2F2000%29

ln%281+%2B+r%29+=+%281%2F8%29%2A+ln%282633.62%2F2000%29

ln%281+%2B+r%29+=+0.0344

1+%2B+r+=+e%5E%280.0344%29

r+=++e%5E%280.0344%29+-+1

r = 0.035 = 3.5%