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Chapter 12: Problem 462

Suppose you buy a 91 -day \(\$ 500,000\) Treasury bill at the price of \(\$ 485,000\) and you hold the bill until it matures. What is the interest rate you earn?

Short Answer

Expert verified
The interest rate earned on the Treasury bill when held until maturity is approximately \(12.03\%\).

Step by step solution

01

Write down the given values

Purchase price: \(\$485,000\) Mature price: \(\$500,000\) Number of days until maturity: \(91\)
02

Calculate the discount rate

To calculate the interest rate, we first need to determine the rate at which the price of the Treasury bill was discounted. The discount rate is calculated as: \(D=\frac{F-P}{F}\) Where: \(D\) = discount rate \(F\) = mature price \(P\) = purchase price \[ D=\frac{500,000-485,000}{500,000} \] Calculating this, we get: \[ D=\frac{15,000}{500,000} = 0.03 \] The discount rate is \(0.03\), or \(3\%\).
03

Calculate the annual discount rate

The current discount rate is for the 91-day period. To calculate the annual discount rate, we need to multiply this by the number of 91-day periods in a year: \(Annualized\:Discount\:Rate = D \times \frac{365}{n}\) Where: \(n\) = number of days until maturity \[ Annualized\:Discount\:Rate = 0.03 \times \frac{365}{91} \] Calculating this, we get: \[ Annualized\:Discount\:Rate = 0.03 \times 4.0110 \approx 0.1203 \] The annual discount rate is approximately \(0.1203\), or \(12.03\%\).
04

Determine the interest rate earned

The interest rate earned is equal to the annual discount rate: \(Interest\:Rate = Annualized\:Discount\:Rate\) Thus, the interest rate earned on the Treasury bill is approximately: \(Interest\:Rate = 12.03\%\) So, by holding the Treasury bill until it matures, you earn an interest rate of approximately \(12.03\%\).

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Most popular questions from this chapter

Suppose a bank acquires an additional \(\$ 1\) of deposits and no required reserve ratio exists. By how much could this one dollar deposit theoretically expand the money supply?

Suppose a commercial bank has deposits of \(\$ 400,000\) and has made loans and investments of \(\$ 315,000 .\) Assume also that deposits are its only source of reserves. If the required reserve ratio is \(20 \%\), how much are its excess reserves?

Suppose that in the banking system as a whole demand deposits are equal to \(\$ 80,000,000\) and reserves are equal to \(\$ 17,000,000\) with a legal reserve ratio of \(10 \%\). If the Federal Reserve doubles the required ratio, by how much will the money-creating potential of the banking system as a whole drop?

If the required reserve ratio, "r," is \(20 \%\), and banks retain excess reserves equal to \(10 \%\), "e," of deposits, calculate the demand deposit multiplier and the total increase in the demand deposits of the banking system as a whole that would result from an initial deposit of \(\$ 10,000\)

What is the FDIC? How does it contribute to financial stability when the general public fears that a bank might fail?
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