Question

Problem #5 (20 pts) s bought an old house to use as his business office. He found that the ceiling was poorly insulated and that the heat loss could be cut significantly if six inches of foam insulation war installed. He estimated that with the insulation, he could cut the heating bill by $150 per month and the air-conditioning cost by $110 per month. Assuming that he uses the AC only from May to September and the heater on peptember and the heater only from December to February. If he decides to install the insulation, it will be done at the beginning of May. James's interest rate is 12% compounded quarterly How much can James spend on insulation if he expects to keep the property for ten years A = 150 pr month - Need P savings por month total = 260 in A-110 pr wooh Al Shanths e llo 4= 3 months @ 1so. 124 1 = 0.0406 = 4.06% N- (10) (12) = 120 1 110 1 no 1 to 1 10 1 11 1 150 156 1 lso p=904,6661 B 10 10/(1.0400) 1 2 20,040 10415 L - ulfz p = 150 / (1.0406) | p=130 L 0.6404 (1.0466) p - 415.79 + 16.040e) S. 1) - 596.51 0.410

Answer 1

12% compounded quaterly for 10 years will get us to effective interest rate of 3% per annum for 40 time period

spending for year 1 starting from may,

heater 110 per month for 5 months= 550

AC for 1 month (dec) 150

total for year 1 = $700

year 2

AC for 3 months (jan, feb and dec) = 150*3 = 450

heater for 5 months = 110 *5 = 550

annual savings from year 2 till 10th year is $1000 per year

to calculate the future value of savings from year 2 till year 10th

PVAF(3%*40) * 1000 - 1000(excluding year 1, as accounting is beginning from 2nd year till 10th year)

(23.115*1000) - 1000 = 22115

PV of first year savings

700* PVAF (3%,2) (2 quarters begining from may)

700*0.942 = 660

thus james should not spend more than (660+22115) $22775 for insulation