a$.$ The spot price of an investment asset is $$30$ and the risk$-$free rate for all maturities is $10\%$ with continuous compounding. The asset provides an income of $$2$ at the end of the first year and at the end of the second year. What is the three$-$year forward price?

b$.$ What should an arbitrager do when the one$-$year forward price of an asset is too low? Assume that the asset provides no income.

c$.$ The current USD$/$euro exchange rate is $1\mathrm{.}4000$ dollar per euro. The six month forward exchange rate is $1\mathrm{.}3950.$ The six month USD interest rate is $1\%$ per annum continuously compounded. Estimate the six month euro interest rate.