Final answer:
An investor must pay no more than $964.29 for a one-year $1,000 t-bill offering a 10% yield to achieve a 12% yield, considering the market interest rate is currently 12%.
Step-by-step explanation:
To determine the price an investor must pay for a t-bill with a 10% yield, we'll calculate the present value of the $1,080 expected payment, factoring in the market interest rate of 12%. When the yield offered by a bond (10%) is less than the market interest rate (12%), investors would expect a discounted purchase price to equate the returns.Using the formula $price = \frac{future\ value}{(1 + market\ interest\ rate)}$, the calculation is $price = \frac{\$1,080}{1 + 0.12} = \frac{\$1,080}{1.12} = \$964.29$. Therefore, an investor should pay no more than $964.29 for the bond to achieve a 12% yield.The concept here is that bonds prices adjust inversely to changes in market interest rates. When new interest rates are higher than a bond's coupon rate, the bond's price drops so investors can achieve equivalent returns on their investments.