Problem 10. Determine at what periodic interest rate a $2000 cash receipt occurr
ID: 2658381 • Letter: P
Question
Problem 10. Determine at what periodic interest rate a $2000 cash receipt occurring at the beginning of year 1 is equivalent to four cash disbursements: a $575 cash disbursement occurring at the end of year 1, a $600 cash disbursement occurring at the end of year 2, a $625 cash disbursement occurring at the end of year 3, and a $650 cash disbursement occurring at the end of year 4. The periodic interest rate is compounded annually. Problem 10. Determine at what periodic interest rate a $2000 cash receipt occurring at the beginning of year 1 is equivalent to four cash disbursements: a $575 cash disbursement occurring at the end of year 1, a $600 cash disbursement occurring at the end of year 2, a $625 cash disbursement occurring at the end of year 3, and a $650 cash disbursement occurring at the end of year 4. The periodic interest rate is compounded annually.Explanation / Answer
From the above table we see that the total PV is 2021 at 8% and 1976 at 9% . So the required Periodic rate is between these two percentages that make the present value = 2000
8% ............ 2021
X % ....... 2000
9% ......... 1976
( X - 8) / (9 - 8) = ( 2000 - 2021 ) / ( 1976 - 2021)
( X - 8 ) = - 21 / - 45
X - 8 = 0.47
X = 8.47 % is the annual interest rate required.
Year CF DF(8%) PV DF(9%) PV 1 575 0.925926 532.4074 0.917431 527.5229 2 600 0.857339 514.4033 0.84168 505.008 3 625 0.793832 496.1452 0.772183 482.6147 4 650 0.73503 477.7694 0.708425 460.4764 Total PV 2021 Total PV 1976