A one-year short forward contract on a non-dividend-paying stock is entered into when the stock price is $144.5 and the risk-free rate of interest is 5% per annum with continuous compounding. The contract is on a share of the stock. Keep four decimal places in your calculation.

a. Calculate the forward price of the contract.

b. What is the value of the contract when it is entered into?

c. Three months later, the price of the stock is $72.7 and the risk-free interest rate is still 5%. Calculate the forward price for a forward contract on the same stock and with the same maturity date as the one entered into in the above question.

d. At this time, calculate the value of the initial contract.

please be detailed as much as possible and write down the formulas