Final answer:
The implied one year forward rate starting in 4 years is found by using the given spot rates of 4-year and 5-year bonds. The calculation involves raising both spot rates to their respective powers, dividing the longer term by the shorter term, and subtracting one. Additionally, the bond's price when its interest rate is lower than the current market rate is determined by discounting the expected future payments by the market interest rate.
Step-by-step explanation:
The implied one year forward rate that starts in 4 years can be calculated based on the current spot rates for the 4-year and 5-year bonds. If the 4-year spot rate is 1% and the 5-year spot rate is 1.5%, we can use the formula for forward rates, which is:
[(1 + spot rate for longer maturity)^longer maturity duration / (1 + spot rate for shorter maturity)^shorter maturity duration] - 1
Applying this formula with the given spot rates gives us the following:
[(1 + 0.015)^5 / (1 + 0.01)^4] - 1
You would calculate this expression to find the one year forward rate that starts in 4 years. Remember that the forward rate reflects the expected future interest rate between two periods i
To understand the concept of bond pricing when its interest rate is less than the market interest rate, consider a bond expected to pay $1,080 in one year. If this bond has an interest rate below the current market rate of 12%, then its price will be determined by the present value of its future payments. Discounting the expected payment using the market interest rate, we can calculate its current price using the formula:
P = Payment / (1 + market interest rate)
So in this example:
P = $1,080 / (1 + 0.12)
Which gives us a price of $964. This means the bond's price will not exceed $964 as you could alternatively invest $964 at the market rate of 12% to receive $1,080 in a year.