Consider an equity index with a continuously compounded dividend yield that is known to vary throughout the year: 4% per annum in February, May, August, and November, and 1% per annum during other months. The continuously compounded risk-free rate is fixed at 5% per annum. a) (5%) Suppose it is now 31 January and that the current index level is 1,000. Calculate the current forward price on the index for delivery on 31 December. b) (5%) Suppose that the index level is 900 on 30 June. Calculate the value of a long position in a forward contract on the index entered on 31 January with delivery on 31 December, and with a contract size of $1 times the index. c) (5%) Suppose that, on 31 July, the forward price on the index for delivery on 31 December is 1,010. Furthermore, on 30 September, the forward price on the index for delivery on 31 December is 910. Calculate the return on the index between 31 July and 31 September