Question

An investor purchased a 91-day, $5000.00 T-bill on its issue date for $4976.44. After holding it for 81 days, she sold the T-bill for a yield of 1.72%.

(a) What was the original yield of the T-bill?
(b) For what price was the T-bill sold?
(c) What rate of retum (per annum) did the investor realize while holding this T-bill?

Answer 1

The original yield of the T-bill was 1.92%, the exact selling price must be calculated using the given yield of 1.72% and the face value, and the rate of return is the annualized profit over the initial investment.

Step-by-step explanation:

Understanding the T-bill Investment

An investor purchased a 91-day T-bill for $4976.44 and sold it after 81 days. To calculate the original yield, we find the difference between the purchase price and the face value of $5000, which is $23.56. The annualized yield is ([$23.56 / $4976.44] * [365 / 91]) = 1.92%.

To calculate the selling price with a yield of 1.72%, we must first find the total interest the new buyer would receive for holding the bill for the remaining 10 days, which is ($5000 * 1.72% * 10/365). This gives us the selling price when subtracted from the face value.

The rate of return for the original investor can be calculated by taking the amount the investor gained and dividing it by the initial investment, then annualizing it over 81 days. This is done by computing the selling price minus the purchase price, dividing by the purchase price, and annualizing the result.