Currently the one-year spot rate is r1 =6%, and the one-year forward rate for a one-year loan maturing at the end of year 2 (1f2) is 6.4%. Similarly, 2f3 = 7.1%, 3f4 = 7.3%, and 4f5 = 8.2%. Show your values at least until second decimal points.

a. What is the spot rates, r2, r3, r4, r5 if the expectation hypothesis holds?

b. Calculate a new bond's price: a five-year bond with the face value of ¥100 paying an annual coupon at 5% (once a year to be paid at the end of the year). We assume that the risk of the bond is reflected by the above term structure.

c. Calculate the yield to maturity of the bond.

d. Calculate the yield to maturity of a five-year annuity product which pays a fixed amount annually starting the end of the year.

e. Calculate the duration of the above five-year bond.

f. When the market interest rate rises by 50 basis points, what do you estimate the change in the price and the new price using the duration estimation model?

g. When the market interest rate decreases by 50 basis points, what do you estimate the change in the price and the new price again using the duration estimation model?

h. When interest rate rise suddenly and the yield curve changed to become a downward curve. Do you think whether or not a shape of downward curve can occur? If so, discuss the reason why this curve may occur.