Question

5. James bought an old house to use as his business office. He found out that the ceiling was poorly insulated and that the heat loss could be cut significantly if six inches of foam insulation were 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 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?

Answer 1

Hi

As described in the question, the total savings in costs per year will $1,000.

The interest rate will be compounded quarterly. Hence, the effective interest rate is shown in the file attached.

James can spend $5,526.06 on insulation.

I have shown both the ways of calculation of present value -

• PV function
• DCF

B C D Year 110 5 550 Α. 1 Savings in AC cost per month 2 Use of AC - No of months 3 Savings in AC cost 4 5 Savings in heating bill per month 6 Use of heater - No of months 7 Savings in AC cost Nm E Savings Present Value $1,000.00 $888.49 $1,000.00 $789.41 $1,000.00 $701.38 $1,000.00 $623.17 $1,000.00 $553.68 $1,000.00 $491.93 $1,000.00 $437.08 $1,000.00 $388.34 $1,000.00 $345.03 $1,000.00 $306.56 $5,525.06 450 1000 9 Total savings per year 10 Period 11 Interest 12 Compounding 13 Effective Interest Rate 14 Present Value of savings. 15 12% Quarterly 12.5509% $5,525.06

With formula-

B C 110 1 Savings in AC cost per month 2 Use of AC - No of months 3 Savings in AC cost =B1*B2 4 150 3 =B5*B6 5 Savings in heating bill per month 6 Use of heater - No of months 7 Savings in AC cost 8 9 Total savings per year 10 Period 11 Interest 12 Compounding 13 Effective Interest Rate 14 Present Value of savings. 15 D E Year Savings 1 1000 2 1000 1000 1000 1000 1000 1000 8 1000 1000 10 1000 Present Value =E2/(1+$B$13)^D2 =E3/(1+$B$13)^D3 =E4/(1+$B$13)^D4 =E5/(1+$B$13)^D5 =E6/(1+$B$13)^D6 =E7/(1+$B$13)D7 =E8/(1+$B$13)^D8 =E9/(1+$B$13)^D9 =E10/(1+$B$13)^D10 =E11/(1+$B$13)^D11 =SUM(F2:F11) 9 =B3+B7 10 0.12 Quarterly =1*(1+B11/4)^4-1 =PV(B13,011,-E2)