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Question 1 (25 points): Refinancing a mortgage You purchased a home (Z+2) years ago for $300,000 and borrowed the entire amount from Broadway Bank at an APR of 3% with monthly payments. The original maturity of your mortgage was (30+X) years. a. (10 points) Draw a time line that depicts the cash flows from the mortgage payments from when you bought your home. i. Show on the time line and compute the outstanding the balance today, and . Give the inputs to your computations for full credit. b. (15 points) The COVID crisis has reduced mortgage rates. Suppose you refinance your mortgage today (repay outstanding amount of old loan and borrow the same amount at a lower rate) with a mortgage maturity equal to the remaining time on your current mortgage, at an APR of 1% and monthly payments. What is the present value of your savings at the prevailing APR if refinancing will incur closing costs of $2500?Table 1 displays the risk-neutral HoLee binomial tree containing the evolution of the continuously compounded one-period rates. Each period in the tree equals six months, that is A = 0.5, Where A denotes the time interval between steps. Recall that such a tree is estimated to t the original term structure of zero coupon bond prices for all maturities. We take p\" = 0-5 as the up-state probability and 1 p" = 0-5 as the down-state probability (recall these are the risk neutral probabilities, not the actual probabilities). Finally, recall the following notation: n+1\5. Question 5 FI'otal: 20 marks] a} The spot price of gold is $1,2DD per ounce. The storage costs are $ 2.? per ounce, to be paid once in 3 months' time. The futures contract on gold has 1 year and 4 months to maturity. and the risk-free rate of interest is [1.3% per year, with continuous compounding. What is the futures price per ounce of gold if it is considered to be an investment asset? (Please display all computations.) [1 0 marks] b} What happens to the size of the convenience yield of a consumption asset, when the total supply of it increases, while the total demand for it remains unchanged? Please choose the correct option and justify your answer. [10 marks] i} Increases ii] Unaffected iii} Decreases