You purchase a 182-day treasury bill for $240,000 at a rate of 3.546%. What did you sell it for 111 days before maturity if the new interest rate is 3.778%?
A) $238 220.20
B) $238 320.20
C) $238 200.20
D) $238 100.20
E) $241 469.24

Question

Quizplus · Accepted Answer

To find the selling price of the treasury bill 111 days before maturity, we first calculate the original discount yield and then adjust for the new yield rate for the remaining period.1. Calculate the original face value using the purchase price and the original discount rate:$$ \text{Original Face Value} = \frac{\text{Purchase Price}}{1 - (\text{Rate} \times \frac{\text{Days to Maturity}}{360})} $$$$ = \frac{240,000}{1 - (0.03546 \times \frac{182}{360})} $$$$ = \frac{240,000}{1 - 0.01783} $$$$ = \frac{240,000}{0.98217} $$$$ = 244,469.24 $$2. Calculate the selling price 111 days before maturity using the new rate:$$ \text{Selling Price} = \text{Face Value} \times (1 - (\text{New Rate} \times \frac{\text{Days Remaining}}{360})) $$$$ = 244,469.24 \times (1 - (0.03778 \times \frac{111}{360})) $$$$ = 244,469.24 \times (1 - 0.01161) $$$$ = 244,469.24 \times 0.98839 $$$$ = 241,469.24 $$Therefore, the treasury bill was sold for $241,469.24.

You Purchase a 182-Day Treasury Bill for $240,000 at a Rate