Question

A proposed solar-heating system for a home costs 6 000 TL and has a rated operational life of 20 years. Purchase and installation of the system is to be financed by a 60-month loan with an annual percentage rate of 7.2 %. The salvage value of the solar-heating system will essentially be zero. Determine the maximum effective yearly heating costs for the system to pay for itself if the annual savings could be invested at 6 % interest compounded annually.

Answer 1

Please refer to the steps shown below:

First we calculate the monthly payment of the loan Present value (PV) 6000 loan duration in months (nper) Rate of interest (r) 7.2% Monthly payment (PMT) =-PMT(Rate/12, nper (60), PV (6000) 119.37

So 119.37 will be the monthly payment of the loan. Now we discount this monthly payment using the reinvestment rate of 6% to find the effective present cost as:

Present value of this 119.37 monthly annuity at 6% per annum =PV(6%/12,60,-119.37) 6174.48 This is the effective present cost of the solar heating system

Finally we can calculate the effective heating costs as:

The annual heating costs can be seen as an annuity at 6% interest that should have the same Present value as the effective cost calculated above So we have PV 6174.48 nper 20 rate 6% PMT 538.32 =PMT(annual rate=6%, nper=20,PV=6174.48)

So the effective annual heating costs should be 538.32

Note that we have used the time value of money functions of Excel for above calculations. They can be done similarly on a financial calculator also. If you need to do manually, you can use the formula for Present value of annuity for these calculations.