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fenix001 [56]
3 years ago
15

If $396 is invested at an interest rate of 13% per year and is compound continuously, how much will the investment be worth in 3

years?
Mathematics
1 answer:
Sveta_85 [38]3 years ago
7 0

Answer:

The investment at the end of the period will be $584.89.

Step-by-step explanation:

FV = PV e⁽ⁿˣ⁾

FV = Future Value = ?

PV = Present Value = $396

n = Interest Rate = 13%

x = time in years = 3

e = mathematical constant = 2.7183

FV = 396 x 2.7183⁽⁰°¹³ ˣ ³⁾

FV = 396 x 1.4770

FV = $584.89

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Answer:

a) 3.47% probability that there will be exactly 15 arrivals.

b) 58.31% probability that there are no more than 10 arrivals.

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}

In which

x is the number of sucesses

e = 2.71828 is the Euler number

\mu is the mean in the given time interval.

If the mean number of arrivals is 10

This means that \mu = 10

(a) that there will be exactly 15 arrivals?

This is P(X = 15). So

P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}

P(X = 15) = \frac{e^{-10}*(10)^{15}}{(15)!} = 0.0347

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(b) no more than 10 arrivals?

This is P(X \leq 10)

P(X \leq 10) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)

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P(X = 3) = \frac{e^{-10}*(10)^{3}}{(3)!} = 0.0076

P(X = 4) = \frac{e^{-10}*(10)^{4}}{(4)!} = 0.0189

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58.31% probability that there are no more than 10 arrivals.

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