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Exotics Faucets and Sinks LTD., guarantees that its new infrared sensor faucet will save any household that has 2 or more children at least $30 per month in water costs beginning 1 month after the faucet is installed. If the faucet is under full warranty for 5 years, the minimum amount a family of four could afford to spend now on such a faucet at an interest rate of 1/2% per year, compounded monthly, is closest to(a) $149c) $1787(b) $1552d) $1890

Respuesta :

TomShelby

Answer:

$1552

Explanation:

it will save 30 per month during 5 years.

we can calculate this as an annuity. So the value of the faucets will be the present value of the cash savings:

[tex]C \times \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]

C $30 saving per month

time 5 years x 12 month per year = 60 months

rate 0.5% = 0.5/100 = 0.005

[tex]30 \times \frac{1-(1+0.005)^{-60} }{0.005} = PV\\[/tex]

PV $1,551.7668

Rounding it will be closest to 1,552

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