A life insurance policy is a financial contract that collects a premium of p per period from the insured and pays out a lump sum benefit B upon the death of the insured. Let m denote the mortality rate, r denote the interest rate and V denote the expected present value of economic profits of the insurance company on this policy. Use the recursive asset pricing formula p + EV' V =! 1+r to express equilibrium life insurance premium, p, through exogenous variables. Explain your answer and show all work. (iii) Loan calculators Suppose that loan of size S is repaid over T periods with equal per-period payments p and interest rate on the loan r. Initial loan size has to be equal to the present value of the payments: S = 1+r' (1+r)2 +...+ (1+ r)T a) Calculate a monthly payment on the following mortgage. Annual interest rate is r = 0.06, mortgage term is 30 years, loan size S = 200,000. (Hint: since you are asked about the monthly payment, present value should be discounted at a monthly frequency. Start with figuring out the monthly interest rate and the mortgage term expressed in months, then apply the formula). b) Jill would like to buy a car that costs S = 20,000. The dealer offers her a 60-month loan with 0 down and a monthly payment p = 421. Calculate the annual interest rate on this loan using Excel. Take the following steps: 1. Generate a column of 40 monthly interest rates, with r = {0.001,0.002,.,0.040}, say column A, starting with Al. 2. Use the geometric series formula to express the present value of payments through p,T and rm, where rm is the monthly interest rate. Plug in the numeric value for p, T and put this formula into cell B1. Have the formula refer to the interest rate from cell Al. Select B1:B100 and press CTRL+D. This will copy the formula and generate a column of present values that correspond to different monthly interest rate. Pick an interest rate from a row whose cell B value corresponds most closely to S. 3. Convert the monthly interest rate rm that you found on step 2 into annual using the compounding formula 1+ ra = (1+ rm)12.