Question

Maintenance on tools in a factory is expected to be $275 at the end of the first year and increase $50 each year for the following 7 years. What approximate present sum of money should be set aside now to pay the maintenance costs for the 8-year period, given that there is an 8% interest rate? What is the equivalent annual cost?

Answer 1

(i) Present worth is computed as follows. Note that

• Maintenance cost in year N = Maintenance cost in year (N - 1) + 50, and
• PV Factor in year N = (1.08)^-N

Year	Maintenance Cost ($)	PV Factor @8%	Discounted Maintenance Cost ($)
	(A)	(B)	(A) x (B)
1	275	0.9259	254.63
2	325	0.8573	278.64
3	375	0.7938	297.69
4	425	0.7350	312.39
5	475	0.6806	323.28
6	525	0.6302	330.84
7	575	0.5835	335.51
8	625	0.5403	337.67
		Present Worth ($) =	2,470.63

(ii) Equivalent annual cost ($) = Present worth / P/A(8%, 8) = 2,470.63 / 5.7466** = 429.93 ~ 430

**From P/A Factor table