A review of personal financial disclosures that Mr. Cruz filed later with the Senate does not find a liquidation of assets that would have accounted for all the money he spent on his campaign. What it does show, however, is that in the first half of 2012, Ted and Heidi Cruz obtained the low-interest loan from Goldman Sachs, as well as another one from Citibank. The loans totaled as much as $750,000 and eventually increased to a maximum of $1 million before being paid down later that year. There is no explanation of their purpose.

Neither loan appears in reports the Ted Cruz for Senate Committee filed with the Federal Election Commission, in which candidates are required to disclose the source of money they borrow to finance their campaigns. Other campaigns have been investigated and fined for failing to make such disclosures, which are intended to inform voters and prevent candidates from receiving special treatment from lenders. There is no evidence that the Cruzes got a break on their loans.

A spokeswoman for Mr. Cruz’s presidential campaign, Catherine Frazier, acknowledged that the loan from Goldman Sachs, drawn against the value of the Cruzes’ brokerage account, was a source of money for the Senate race. Ms. Frazier added that Mr. Cruz also sold stocks and liquidated savings, but she did not address whether the Citibank loan was used.