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.

Answer 1

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

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.