Using the spot rates calculate the price and ytm of a

Question

The term structure of interest rates (i.e., the spot rate yield curve) currently looks like this:

1-year 1%

2-year 2.5%

3-year 3.5%

4-year 4.25%

a. From these rates there are 6 different forward rates that you can derive. Calculate all of them. Use the notation in my notes in which sft stands for a forward rate beginning in s years and lasting for t years.

b. Using the spot rates, calculate the price and ytm of a 4-year bond that pays a 4.125% coupon rate (assume annual payments).

c. Suppose that you hold this bond to maturity. Each time you receive a coupon payment, you reinvest it in an investment that matures at the same time that the bond does and also allows your reinvested coupon to grow at the same rate as the bond’s ytm. Calculate the total amount of cash that you will have accumulated as of the day that the bond makes its final payment. Include in this total the final coupon and principal payment of the bond as well as money accumulated from reinvesting coupons along the way. Given the price that you paid for this bond (in part b) and given the total amount of cash that you have 4 year later, what was your average annual compound rate of return?

d. Suppose again that you hold this bond to maturity. Each time you receive a coupon payment, you reinvest it in an investment that matures at the same time that the bond does and also allows your reinvested coupon to grow. However, this time, assume that the reinvested coupons grow at the following rates:

1^st coupon payment grows at 5.356%

2^nd coupon payment grows at 6.030%

3^rd coupon payment grows at 6.533%

Calculate the total amount of cash that you will have accumulated as of the day that the bond makes its final payment. Include in this total the final coupon and principal payment of the bond as well as money accumulated from reinvesting coupons along the way. Given the price that you paid for this bond (in part b) and given the total amount of cash that you have 4 year later, what was your average annual compound rate of return? Compare and comment on your answer here and in part d.