HOUSTON — Oil prices settled 5 percent higher on Monday after Iran and the United States traded demands for compensation, dimming prospects for a deal to reopen the Strait of Hormuz. Iran also said the U.S. must lift sanctions on Tehran, and meet a number of other conditions for reopening the vital waterway, while U.S. President Donald Trump said Iran must pay compensation for "all of the people that they have killed and gravely wounded." Brent crude futures settled up $4.17, or 4.99 percent, at $87.72 a barrel, while U.S. West Texas Intermediate crude futures closed $3.95, or 5.05 percent, at $82.13. The percentage gains were the highest since July 29 on both contracts. Both benchmarks fell more than 7 percent last week on hopes that Iran and Oman were close to reaching a deal that would result in a reopening of the strait, which carried a fifth of the world's oil and liquefied natural gas before the start of the Middle East conflict in late February. Iran said it was nearing a final pact with Oman to define new shipping lanes through the strait but repeated that the U.S. must meet