On a certain date, Pat invested $7,000 at x percent annual interest, compounded annually. If the total value of the investment plus interest at the end of 10 years will be $28,000, in how many years total will the total value of the investment plus interest increase to $56,000? Options.
A) 15
B) 16
C) 18
D) 20
E) 24
28,000 = 7,000(1 + x)^10   4 = (1+x)^10 = 2^2   (1+x)^10 = ((1+x)^5)^2 = 2^2   Therefore, (1+x)^5 = 2   56,000 = 7,000(1 + x)^n   (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 $7,000 at x percent annual interest, compounded annually. If the total value of the investment plus interest at the end of 10 years will be $28,000, in how many years total will the total value of the investment plus interest increase to $56,000?