Question

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 quarter is $3,500, 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 9% per year, compounded continuously?

Answer 1

Answer: Developers can spend $55316.9

Explanation:

EAR =$[e^{Annual percentage rate} -1]\times 100$

Effective Annual Rate=$(e^{(9/100)} -1)\times 100$

Effective Annual Rate% = 9.42

$PV_{Ordinary Annuity} = C\times [\frac{(1-(1+\frac{i}{100} )^{-n} )}{(i/100)} ]$

where;

C = Cash flow per period

i = interest rate

n = number of payments

$PV = 3500\times [\frac{(1-(1+\frac{9.42}{400} )^{-5\times 4} )}{(9.42/400)} ]$

PV =  $55316.9