a. What is the relationship between discounting and compounding? b. What is the relationship between the present-value factor and the annuity present-value factor? c. i. What will $3,800 invested for 11 years at 14 percent compounded annually grow to? ii. How many years will it take $410 to grow to $1,032.45 if it is invested at 8 percent compounded annually? iii. At what rate would $1,900 have to be invested to grow to $90,086.83 in 26 years? d. Calculate the future sum of $1,200, given that it will be held in the bank for 19 years and earn 17 percent compounded semiannually. e. What is an annuity due? How does this differ from an ordinary annuity? f. What is the present value of an ordinary annuity of $1,600 per year for 29 years discounted back to the present at 13 percent? What would be the present value if it were an annuity due? g. What is the future value of an ordinary annuity of $1,600 per year for 29 years compounded at 13 percent? What would be the future value if it were an annuity due? h. You have just borrowed $230,000, and you agree to pay it back over the next 15 years in 15 equal end-of-year navments plus 8 percent compound interest on the unpaid balance What will be the size of these navments? $ 16059.68 (Round to the nearest cent.) ii. How many years will it take $410 to grow to $1,032.45 if it is invested at 8 percent compounded annually? years (Round to the nearest whole number.)