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KATRIN_1 [288]
3 years ago
9

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?
Business
1 answer:
Colt1911 [192]3 years ago
7 0

Answer: <em><u>Developers can spend $55316.9</u></em>

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

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