Additional Problems: Karen makes deposits of X at the beginning of each year for 10 years. She uses the funds in her account to purchase a perpetuity with payments starting six years after the final deposit paying 70 every year. The annual effective interest rate is 8%. Calculate X. 1. Ray wants to accumulate 8,000 at the end of 20 years. At the end of each year for the first 10 years he deposits 150. At the end of each year for the next 10 years he deposits X. The annual effective interest rate is 5%. Calculate X. 2. . An investment requires an initial payment of 10,000 and annual payments of 1,000 at the end of each of the first 10 years. Starting at the end of the eleventh year, the investment returns five annual payments of X. The annual effective interest rate is 10%. DetermineX. 4. Susan and Jeff each make deposits of 100 at the end of each year for 40 years. Starting at the end of the 41st year, Susan makes annual withdrawals of X for 15 years and Jeff makes annual withdrawals of Y for 15 years. Both funds have a balance of 0 after the last withdrawal. Susan's fund earns an annual effective interest rate of 8%. Jeff's fund earns an annual effective interest rate of 10%. Calculate Y-X