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The ask discount rate on a particular money market instrument is 3.75%. The face...
Mar 16, 2024
The ask discount rate on a particular money market instrument is 3.75%. The face value is 200,000anditmaturesin51days.Whatisitscurrentprice?Whatwouldbethecurrentpriceifithad71daystomaturity?(b)Whatwouldbeyouraskdiscountrate162−dayTreasurybillfor200,000 and it matures in 51 days. What is its current price? What would be the current price if it had 71 days to maturity? (b) What would be your ask discount rate % and bond equivalent rate % on the purchase of a 162-day Treasury bill for 4,875 that pays $5,000 at maturity?
Answer
The current price of the money market instrument with 51 days to maturity is 198,537.50,andwith71daystomaturity,itis198,537.50, and with 71 days to maturity, it is 198,212.50. The ask discount rate on the purchase of a 162-day Treasury bill is 3.07%, and the bond equivalent rate is 6.23%.
Solution
a
Current Price Calculation for 51 days: The current price is calculated using the formula P=FV×(1−d×t360) P = FV \times \left(1 - \frac{d \times t}{360} \right) where P P is the current price, FV FV is the face value, d d is the discount rate, and t t is the time to maturity in days
b
Current Price for 51 days: Using the formula, P=200,000×(1−0.0375×51360)=200,000×(1−0.00520833)=200,000×0.99479167=$198,537.50 P = 200,000 \times \left(1 - \frac{0.0375 \times 51}{360} \right) = 200,000 \times (1 - 0.00520833) = 200,000 \times 0.99479167 = \$198,537.50
c
Current Price Calculation for 71 days: Using the same formula with t=71 t = 71 days, P=200,000×(1−0.0375×71360)=200,000×(1−0.00739583)=200,000×0.99260417=$198,212.50 P = 200,000 \times \left(1 - \frac{0.0375 \times 71}{360} \right) = 200,000 \times (1 - 0.00739583) = 200,000 \times 0.99260417 = \$198,212.50
d
Ask Discount Rate Calculation: The ask discount rate is calculated using the formula d=FV−PFV×360t d = \frac{FV - P}{FV} \times \frac{360}{t} where P P is the purchase price of the Treasury bill
e
Ask Discount Rate for Treasury bill: Using the formula, d=5,000−4,8755,000×360162=0.025×2.22222222=0.0307 or 3.07% d = \frac{5,000 - 4,875}{5,000} \times \frac{360}{162} = 0.025 \times 2.22222222 = 0.0307 \text{ or } 3.07\%
f
Bond Equivalent Rate Calculation: The bond equivalent rate (BER) is calculated using the formula BER=FV−PP×365t BER = \frac{FV - P}{P} \times \frac{365}{t}
g
Bond Equivalent Rate for Treasury bill: Using the formula, BER=5,000−4,8754,875×365162=0.02564103×2.25308642=0.0623 or 6.23% BER = \frac{5,000 - 4,875}{4,875} \times \frac{365}{162} = 0.02564103 \times 2.25308642 = 0.0623 \text{ or } 6.23\%
Key Concept
Discount Rate and Bond Equivalent Rate
Explanation
The discount rate is the percentage reduction from the face value of a bill, reflecting the interest cost to the purchaser. The bond equivalent rate is an annualized version of the discount rate, adjusted for a 365-day year, providing a comparable rate to bonds with semiannual interest payments.
Key Concept
Current Price of Money Market Instruments
Explanation
The current price of a money market instrument is calculated by discounting its face value by the discount rate over the period until maturity, adjusted for a 360-day year, which is a banking convention.
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