Hello, I am preparing for my midterm exam and do not know how to solve these questions:

3.1 A $ 50 stock pays a dividend of $1 every 3 months, with the rst dividend coming 3
Months from today. The continuously compounded interest rate is 3%.
(I) What is the forward price of this stock with expiry 1 year from today? (The forward
Is to purchase the stock ex-dividend, I.e. The purchaser under the forward does not
Receive the dividend being paid at expiry.)
(ii) Suppose you were able to go long or short this forward for a forward price $ 1 less
Than your answer in part (I). Describe in detail the arbitrage that could be done.

3.2 Repeat Question 3.1, replacing the stock by a foreign currency, with spot price $ 7.8,
And which pays interest at 4%, continuously compounded.

3.4 Take rD = 5% (\domestic" interest rate), rF = 6% (\foreign" interest rate), both
Continuously compounded. Also take the spot price S of the \foreign dollar" to be 1
\domestic" dollar.
(I) What is the no-arbitrage 1 year forward price of the F$ (\foreign dollar"), in D$s
(\domestic dollars")?
(ii) If the forward price of the foreign dollar were D$ 0.1 HIGHER than in Part (I),
Then describe the arbitrage you could implement.
(iii) The forward price of the foreign dollar were D$ 0.1 LOWER than in Part (I),
Then describe the arbitrage you could implement.


THANKS in advance! Urgent help much appreciated!