A one year long forward contract on an investment asset is entered into when the spot price of the asset is $30. This asset provides an income of $2 at the end of the 3-month and $2 at the end of the 9-month. The risk free rate for all maturities (with continuous compounding) is 10%.

a. What is the forward price?

b. What is the initial value of the forward contract?

c. Six months later, the price of the asset is $35 and the risk-free rate is still 10%. What is the forward price at this time?

d. What is the value of the forward contract at the end of six months?