Time Value Analysis - Pensacola Surgery Center Case 12 Cases in Healthcare Finance - Louis C. Gapenski. 4. Now consider a second alternative for accumulating funds to buy the new billing system. In lieu of a lump sum investment, assume that five annual payments of $32,000 are made at the end of each year. d) What annual interest rate is required to accumulate the $ 200,000 needed to make the purchase,assuming a 32,000 annual payment? e) What size annual payement is needed to accumulate $200,000 under annual compounding at a 10% interest rate.