Four years ago, Lucas invested $500. Three years ago, Matt invested $600. Today, these two investments are each worth $800. Assume each account continues to earn its respective rate of return and interest is compounded annually. Which one of the following statements is correct concerning these investments? Show your answer.

i. Three years from today, Matt's investment will be worth more than Lucas's investment.

ii. One year ago, Lucas's investment was worth less than Matt's investment.

iii. Matt earns a higher rate of return than Lucas.

iv. Matt has earned an average annual interest rate of 9.86 percent.

v. Lucas has earned an average annual interest rate of 12.64 percent.