On a certain date, Pat invested $5,000 at x percent annual interest, compounded annually. If the total value of the investment plus interest at the end of 10 years will be $20,000, in how many years total will the total value of the investment plus interest increase to $40,000?
Choose the correct option:
A) 15  B) 16  C) 18  D) 20  E) 24
5,000(1 + x)^10 = 20,000   (1+x)^10 = 4 = 2^2   (1+x)^10 = ((1+x)^5)^2 = 2^2   Therefore, (1+x)^5 = 2   5000(1 + x)^n = 40,000   (1+x)^n = 8   (1+x)^n = 2^3   (1+x)^n = ((1+x)^5)^3 = (1+x)^15   Therefore, n = 15.   The answer is 15.
<result>A</result>
On a certain date, Pat invested $5,000 at x percent annual interest, compounded annually. If the total value of the investment plus interest at the end of 10 years will be $20,000, in how many years total will the total value of the investment plus interest increase to $40,000?