annual rate of compound interest

Question

When you were ten years old, your parents invested $5,000 for your future. You are now thirty and, with interest compounding quarterly, the initial $5,000 has accumulated to $8,231 over the 20 years. What annual rate of compound interest was used?

Answer 1

8231 = 5000(1+r)^20

8231/5000 = (1+r)^20

(8231/5000)^(1/20) = 1+r

r =(8231/5000)^(.05)- 1

r=1.025 -1

r= .025 = 2.5% interest rate compounded annually