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Bogdan [553]
4 years ago
8

If $8500 is invested at 12.7% compounded continuously, the future value S at any time t (in years) is given by the following for

mula. (Round your answers to two decimal places.) S = 8500e0.127t
(a) What is the amount after 18 months? S = $

(b) How long before the investment doubles? t = yr
Mathematics
1 answer:
Serjik [45]4 years ago
8 0

Answer:

Given formula is :

S = 8500e^{0.127t}

We have p = 8500

r = 12.7% or 0.127

(a) when t = 18 months or \frac{18}{12}=1.5 years

S = 8500e^{0.127(1.5)}

=8500e^{0.1905}

=e^{0.1905}= 1.20985

S = $10283.73

(b) Investment doubles means S = 8500\times2=17000

17000=8500e^{0.127t}

\frac{17000}{8500}=e^{0.127t}

=> 2=e^{0.127t}

Taking log on both sides

ln(2)=ln(e^{0.127t})

We get t = 5.45 years

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