The risk-free investment rates at 1, 2, 3, 4 and 5 years respectively are assumed to be 2%, 3%, 3.7%, 4.2% and 4.5%.

a) Give the current value of a flow that brings in 100 euros at the end of each of these 5 years.

b) Give the current value of the forward rates for an investment with a maturity (i.e. duration) of one year in the first, second, third, fourth and fifth year.

c) We consider a bond with nominal 100, coupon rate c, maturity 5 years and redemption value equal to the nominal (it is therefore a flow where we pay 100 on date 0, and receive c 100 at each date k, k = 1, 2, 3, 4 and 5 plus another 100 at date 5).

Determine the value of c that will make its current price zero.