6.9
0 = -65,220(P/A,i,4) + (57,925 – 35,220)(P/A,i,31)(P/F,i,4)
0 = -65,220(P/A,i,4) + (22,705)(P/A,i,31)(P/F,i,4)
Solve by trial and error:
Try 6%:
0 = -225,994 + 250,510 = $24,516
i too low
Try 7%:
0 = -220,913 + 217,071 = -$3842
i too high
i = 6.86% per year
(spreadsheet)
6.10
0 = -1537(P/A,i,48) + (2057 – 1537)(P/A,i,240)(P/F,i,48)
0 = -1537(P/A,i,48) + (520)(P/A,i,240)(P/F,i,48)
Solve by trial and error or spreadsheet:
(a) i = 0.39% per month
(spreadsheet)
(b) i = 0.39*12 = nominal 4.68% per year
6.11
0 = -100 – 400(100,000) + 20(P/A,i,10)
(millions)
0 = -140 + 20(P/A,i,10)
(P/A,i,10) = 7.000
From 7% and 8% tables, i is slightly over 7%
i = 7.07% per year
(spreadsheet)
6.12
0 = -5(6000) + 600(P/A,i,156)
(P/A,i,156) = 50.0000
Solve for i by trial and error or spreadsheet:
(a) i = 1.89% per week
(spreadsheet)
(b) i = 1.89*52 = nominal 98.3% per year
6.13
Spending $60,000 now will result in savings of $28,000 in years 0, 3 and 6. The
rate of return equation is :
0 = -60,000 + 28,000 + 28,000[(P/F,i,3) + (P/F,i,+6)]
0 = -32,000 + 28,000[(P/F,i,3) + (P/F,i,+6)]
Solve for i by trial and error or spreadsheet:
i = 13.7% per year
(spreadsheet)
6.14
0 = -500 + 0.18(2500)(P/F,i,2) + 500(1.62)(P/A,i,5)(P/F,i,5) – 10(P/A,i,10)
0 = -500 + 450(P/F,i,2) + 810(P/A,i,5)(P/F,i,5) – 10(P/A,i,10)
Solve for i by trial and error or spreadsheet:
i = 42% per year
(spreadsheet)
6- 2