Question

4. Because of a chronic water shortage in California, new athletic fields must use artificial turf or xeriscape landscaping. If the value of the water saved each six-months is $5,500, how much can a private developer afford to spend now on artificial turf provided he must recover his investment in 5 years. Use an interest rate of 10% per year, compounded continuously?

please type out if possible easier to read

Answer 1

Total number of periods for savings to occur = 5 x 2 = 10 half years

Saving each half year = 5500

Rate of interest per half year = e^(10%/2) - 1 = 5.1271%

Amount required now = 5500 x (P/A, 5.1271% , 10)

= 5500 * 7.6743

= $42,208.65

This is the required amount.