1. (a) Suppose a principal R is invested at regular intervals, compounding at a rate R% in each period, over N periods. Moreover, assume that your compounding period occurs three times more frequently than your deposits (for example, if you invest quarterly but compound monthly), and that N is divisible by 3. Write out a sum which describes the present value of this investment, then use the formula for a finite geometric series to reduce this to a formula without sums. (b) Suppose UTM issues bonds with a one-year maturity and $1000 face value on January 1, 2019. These bonds pay quarterly coupons of $50 on April 1, 2019; July 1, 2019: October 1, 2019; and January 1, 2020. Compute the present value of this annuity in two ways: First by using simple compounding interest to bring back each individual payment, then confirm your answer by using the annuity formula you found in part (a). Assume an APR of 1.3%. Formulas for finite geometric series: 1+c+2+3+...+ -+ -1 = c+2+3+...+ +"-1 + (=