If the effective annual yield of the U.S. T-Bill is 4.75% and the U.S. T-Bill holding period yield is 0.0065, the corresponding U.S. T-Bill has ______ days until maturity.

Explanation: The effective yield quote for a U.S. T-Bill is calculated as follows: EAY = (1+HPY)^(365/t)-1, where: EAY = effective annual yield, HPY = holding period yield, and t = days until maturity. Therefore, we can write HPY = (1+EAY)^(t/365) - 1.

It follows: 0.0065 = (1+0.0475)^(t/365) - 1 or 1.0065 = (1.0475)^(t/365). Using the natural logarithm (ln), we can write: ln(1.0065) = (t/365) ln(1.0475). It follows that t = 365 x ln(1.0065) / ln(1.0475) = 50.96, or approximately 51 days.