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777dan777 [17]
3 years ago
12

Stan has made a $125.30 monthly deposit into an account that pays 1.5% interest, compounded monthly, for 35 years. He would now

like to draw a monthly salary from the account. Determine the amount that Stan can withdraw each month for 20 years, if he plans on not having anything in the account at the end of the 20 year period and no future deposits are made to the account.
Mathematics
2 answers:
MissTica3 years ago
7 0
The future value of a monthly deposit A=125.30 at annual interest i=0.015 per annum for n=35 years compounded monthly is given by
FV=A((1+i/12)^(12*n)-1)/(i/12)
=125.30(1+0.015/12)^(12*35)/(0.015/12)
=$69156.05

The annuity formula is given by
Payment = r(PV)/(1-(1+r)^(-n))
where
r=interest rate per period = 0.015/12
PV= $69156.05
n=20*12=240
so
Payment = (0.015/12)<span>69156.05/(1-(1+0.015/12)^(-240))
= $333.71  per month.</span>
aliina [53]3 years ago
4 0

Answer:

It is D. $333.71

Step-by-step explanation:

I got it in the test

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The distribution of weekly salaries at a large company is right skewed with a mean of $1000 and a standard deviation of $350. Wh
Shtirlitz [24]

Answer:

68.76% probability that the sampling error made in estimating the mean weekly salary for all employees of the company by the mean of a random sample of weekly salaries of 50 employees will be at most $50

Step-by-step explanation:

To solve this question, we have to understand the normal probability distribution and the central limit theorem.

Normal probability distribution:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central limit theorem:

The Central Limit Theorem estabilishes that, for a random variable X, with mean \mu and standard deviation \sigma, a large sample size can be approximated to a normal distribution with mean \mu and standard deviation, which is also called standard error s = \frac{\sigma}{\sqrt{n}}

In this problem, we have that:

\mu = 1000, \sigma = 350, n = 50, s = \frac{350}{\sqrt{50}} = 49.5

What is the probability that the sampling error made in estimating the mean weekly salary for all employees of the company by the mean of a random sample of weekly salaries of 50 employees will be at most $50

This is the pvalue of Z when X = 1000+50 = 1050 subtracted by the pvalue of Z when X = 1000-50 = 950. So

X = 1050

Z = \frac{X - \mu}{\sigma}

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{1050-1000}{49.5}

Z = 1.01

Z = 1.01 has a pvalue of 0.8438

X = 950

Z = \frac{X - \mu}{s}

Z = \frac{950-1000}{49.5}

Z = -1.01

Z = -1.01 has a pvalue of 0.1562

0.8438 - 0.1562 = 0.6876

68.76% probability that the sampling error made in estimating the mean weekly salary for all employees of the company by the mean of a random sample of weekly salaries of 50 employees will be at most $50

4 0
2 years ago
tuckers score in a video game was changed by -75 points because he missed some targets. he got -15 for each missed target. how m
Cerrena [4.2K]
He missed 5 targets because if you multiply 15 by 5 you get 75
8 0
3 years ago
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