Question

Suppose the 4-year spot rate equals r4​=4.2% and the 1-year forward rate over the 5 th year is 5.2%. Compute r5​, the 5 -year spot rate. (Assume all rates in this question are expressed in semi-annual compounding.) % Question 3: (1 point) Suppose you are trying to construct the yield curve, and you have the following data If an 18-month bond with a 7.8% coupon is trading at 105.75, compute the 18 -month spot rate.

Answer 1

The present value of the bond is $3,057.18 with an 8% discount rate and $2,769.17 with an 11% discount rate.

Step-by-step explanation:

To calculate the present value of the bond, we need to discount each future cash flow using the given discount rate. In this case, the bond pays $240 at the end of the first year and $3,240 ($240 interest + $3,000 principal) at the end of the second year. To calculate the present value, we divide each cash flow by (1 + discount rate)^n, where n is the number of periods. Using a discount rate of 8%, the present value of the bond is calculated as follows:

PV = (240 / (1 + 0.08)^1) + (3240 / (1 + 0.08)^2)

PV = 222.22 + 2834.96

PV = $3057.18

If the discount rate is increased to 11%, the present value of the bond is calculated as follows:

PV = (240 / (1 + 0.11)^1) + (3240 / (1 + 0.11)^2)

PV = 215.32 + 2553.85

PV = $2769.17