D. AP510 c. mp3mi/ d. kpsat/ e none of these 17. A perpetuity pays 100 per year. Immediately after the fifth payment, the perpetuity is exchanged for a 25 year annuity-immediate that will pay X each beginning at the end of the first year. Set up an equation for X if the annual interest rate is i. 18. John deposits 100 into an account at the beginning of each 4-year period for 40 years. The account credits interest at an annual effective interest rate of i. Suppose 5A(20) = A(40), where A (20) is the accumulation at the end of 20th year (right before the next payment). Set up an equation for solving 2 where x =1+j is the 4-year future value factor. 19. Smith deposits 100 each into an account that earns 12% nominal annual rate compound monthly at the end of each month for 12 months. He wants to deposit X per month for the next 12 months so that he'll have exactly 2000 right after the last deposit. Set up an equation for X 20. Smith deposits X each at time (year) 2.4,...,10 and Y each at time 1,3.....9 into an account that earns effective annual rate i. Find an expression for the total accumulation right after the last deposit and simplify it as much as possible