You are given:

(i) The current price of a stock is 1,000.

(ii) The stock pays dividends continuously at a rate proportional to its price.

(iii) The continuously compounded risk-free interest rate is 5%.

(iv) a 6-month forward price of 1,020 is observed in the market.

Describe actious you could take to exploit an arbitrage opportunity and calculate the resulting profit (per stock unit) in each of the following cases:

(a) The dividend yield of the stock is 0.5%

(b) The dividend yield of the stock is 2%