Q.3a Suppose that one takes a mortgage loan for the amount L that is to be paid over n months with equal payments of A at the end of each month. The interest rate for the loan is r per month, compounded monthly. In terms of L,n and r, what is the value of A ? [6] Q.3b Explain with appropriate mathematical details as what do you understand by rate of return on an investment. If the interest rate is continuously varying, then derive the formula to calculate the present value function, P(t). [2+5] Q.3c Explain the difference between an American put option and a European put option. When will these two options be equivalent? If you are given a choice to buy any of these two options (if the option value is same for both, which is very unlikely but you may be lucky that day) then which one will you buy and why? [2+1+1+1]