Calculate the effect on the equilibrium interest rate in this market, as a result of the Federal Reserve action. The expected interest rate on a one-year discount bond will decrease increase decrease to 22%. (Round your intermediate calculations to the nearest whole number. Round your final answer to two decimal places.)
The correct answer and explanation is:
To answer this question, we need to apply the bond pricing and interest rate relationship. While the question is partially incomplete, it seems to refer to the effect of Federal Reserve actions (like bond purchases) on the equilibrium interest rate in the bond market.
Let’s assume the following typical scenario based on how the Federal Reserve usually operates:
Scenario Assumption:
- The Federal Reserve buys bonds in the open market (expansionary monetary policy).
- As a result, bond prices increase.
- When bond prices rise, interest rates (yields) fall.
This inverse relationship between bond prices and interest rates is key.
Step-by-Step Calculation:
Let’s say we are dealing with a one-year discount bond (zero-coupon bond). Suppose:
- Face value (FV) = $100
- Expected price (P) = price paid for the bond today
- The interest rate (i) is calculated by:
i=FV−PPi = \frac{FV – P}{P}
Given:
The interest rate will decrease to 22%.
We use this to find the new bond price: 0.22=100−PP0.22 = \frac{100 – P}{P}
Multiply both sides by PP: 0.22P=100−P0.22P = 100 – P
Add PP to both sides: 1.22P=1001.22P = 100 P=1001.22≈81.97P = \frac{100}{1.22} \approx 81.97
Final Answer:
New bond price = $81.97
New equilibrium interest rate = 22.00%
Explanation (300 words):
The Federal Reserve, as the central bank, influences the money supply and interest rates through open market operations—primarily by buying or selling government bonds. When the Fed wants to stimulate the economy, it buys bonds, which increases demand for bonds. As demand for bonds increases, their prices rise.
This price rise causes the yield (or interest rate) on bonds to fall, because investors are paying more upfront for the same return at maturity. For example, a one-year discount bond with a face value of $100 that previously sold for $82 would yield a higher return than the same bond now selling for $91. The formula for the yield on a discount bond is: Interest Rate (i)=Face Value−PricePrice\text{Interest Rate (i)} = \frac{\text{Face Value} – \text{Price}}{\text{Price}}
Given the Fed’s action, the bond price rises, and the interest rate drops. When we plug in the numbers and solve for the new price, we find the bond now sells for $81.97, implying a yield (interest rate) of 22.00%.
This change reflects a new equilibrium interest rate in the bond market, where the quantity of money supplied and demanded balances. The Fed’s intervention effectively lowers market interest rates to encourage borrowing, investing, and spending in the broader economy.
Answer: The new equilibrium interest rate is 22.00%.