please answer a-d corrctly for upvote

2-58. In this exercise, we'll determine how to modify the annuity formula to account for discrepencies in the compounding and deposit periods. In each case, suppose a principal R is invested at regular intervals, compounding at a rate R% in each period, over N periods. (a) Suppose your deposits occur three times more frequently than your compounding period (for example, if you invest monthly but compound quarterly). 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) Generalize part (a) by considering the situation where you deposit k-times more frequently than your compounding period. (c) Suppose your componding 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. (d) Generalize part (a) by considering the situation where you compound k-times more frequently than your deposit period. Again, you may assume that N is divisible by k