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A bank account earned 3.5% continuously compounded annual interest. After the initial deposit, no deposits or withdrawals were m

aalyn [17]

This question is incomplete. Below is the complete question:

A bank account earned 3.5% continuously compounded annual interest. After the initial deposit, no deposits or withdrawals were made. At the end of an 8 year period, the balance in the account was $13231.30. what is the amount of the initial deposit?

Answer: The initial deposit is $10,001

Step-by-step explanation:

To solve this we need to utilize the continuous compounding interest formula:-

Fv = Pv × e^(i × t)

Where, Fv = the future value

Pv = present value

i = the interest rate

t = the time in years

e = a mathematical constant that is usually approximated by 2.7183

In this case, the Fv = 13,231.30

i = 3.5% or 0.035

t = 8 years

e = 2.7183

Pv = ? (The unknown variable).

13,231.30 = Pv × [2.7183^(0.035 × 8)]

13,231.30 = Pv × [2.7183^(0.28)]

13,231.30 = Pv × 1.323

Pv = 13,231.30/1.323

Pv = $10000.98

= $10,001

Therefore the initial deposit is $10,001

8 0

2 years ago

The number of defective components produced by a certain process in one day has a Poisson distribution with a mean of 20. Each d

Kruka [31]

Answer:

The probability that exactly 15 defective components are produced in a particular day is 0.0516

Step-by-step explanation:

Probability function : $P(X=x)=e^{-\lambda} \frac{\lambda^x}{x!}$

We are given that The number of defective components produced by a certain process in one day has a Poisson distribution with a mean of 20.

So, $\lambda = 20$

we are supposed to find the probability that exactly 15 defective components are produced in a particular day

So,x = 15

Substitute the values in the formula :

$P(X=15)=e^{-20} \frac{20^{15}}{15!}$

$P(X=15)=0.0516$

Hence the probability that exactly 15 defective components are produced in a particular day is 0.0516

8 0

2 years ago

Write the decimal 1,072.039 in words

Rina8888 [55]

One thousand seventy two point thirty nine thousandths.

3 0

2 years ago

If each lap in a pool is 100 meters long, how many laps equal one mile? Round to the nearest tenth. (Hint: 1 foot ≈0.3048 meter)

aalyn [17]

If each lap in a pool is 100 meters long,how many laps equal one mile Round to the nearest tenth.(Hint:1 foot=0.3048 meter) 1 mile = 5280 ft lets do a ratio: 1ft/.3034m = x ft/100m the ft and meters sybols cancel, so 1/.3048 =x/100 so 100/.3038 = x = 329.164 so there are 329.164 ft for every 100 meters to find the number of laps to get to a mile which is 5280, do another ratio 329.164ft/100 m =5280 ft/xm the left side reduces to 3.29164 =5280/x you can compute this and see that 5280/3.29164 = 1604.064 meters 1604.064 meters *1 lap / 100m = 16.04064 laps are required to make a mile

7 0

2 years ago

Triangle XYZ has vertices X(–1, –1), Y(–2, 1), and Z(1, 2). What is the approximate measure of angle Z?

Molodets [167]

The answer to this question is A. 37.2°

8 0

2 years ago

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