Question

The Gentle Warming Company is purchasing a new cooling system. To pay for the system, the company agrees to make 12 installment payments of $5133 per year, beginning at the end of year 1. The company also has to pay a system fee of $2298 that will begin at the end of year 1 and decrease by $155 per year until the system is paid off. How much should the company set aside today to pay for the cooling system if the bank pays 3% per year compounded annually?

Answer 1

Annual total cost = Installment payment + System fee

PV factor in year N = (1.03)^-N

Present worth (PW) of total cost is computed as follows.

Year	Installment ($)	System Fee ($)	Total cost ($)	PV Factor @3%	Discounted Total cost ($)
	(A)	(B)	(C)=(A)+(B)	(D)	(C)x(D)
1	5,133	2,298	7,431	0.9709	7,215
2	5,133	2,143	7,276	0.9426	6,858
3	5,133	1,988	7,121	0.9151	6,517
4	5,133	1,833	6,966	0.8885	6,189
5	5,133	1,678	6,811	0.8626	5,875
6	5,133	1,523	6,656	0.8375	5,574
7	5,133	1,368	6,501	0.8131	5,286
8	5,133	1,213	6,346	0.7894	5,010
9	5,133	1,058	6,191	0.7664	4,745
10	5,133	903	6,036	0.7441	4,491
11	5,133	748	5,881	0.7224	4,249
12	5,133	593	5,726	0.7014	4,016
				PW of Cost ($) =	66,025

Money to be set aside today = $66,025