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Cloud [144]
2 years ago
6

Michael is planning to invest his 2,000 into a bank account between investment A with 8% simple interest or investment B with 6%

compound interest. He also plans to invest his money for 12 years. Which investment should be choose to get the biggest return​
Mathematics
1 answer:
Angelina_Jolie [31]2 years ago
3 0

The investment with the bigger return is investment B.

<h3>What is simple interest and compound interest?</h3>

Simple interest rate is the interest that is paid only on the principal portion of a loan. This means that the debtor does not pays interest on the interest rate already accrued. This differs from compound interest where the debt holder pays interest on the principal and the interest rate already accrued

<h3>What is the compound interest?</h3>

The formula for calculating future value:

FV = P (1 + r)^n

  • FV = Future value
  • P = Present value
  • R = interest rate
  • N = number of years

2000 x (1.06)^12 = $4024.39

Compound interest =  $4024.39 - $2000 =  $2024.39

<h3>What is the simple interest? </h3>

Simple interest = principal x time x interest rate

2000 x 0.08 x 12 = $1920

To learn more about future value, please check: brainly.com/question/18760477

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2 years ago
Consider the question of whether the home team wins more than half of its games in the National Basketball Association. Suppose
spayn [35]

Answer:

0.0037 = 0.37% probability that the home team would win 65% or more of its games in a simple random sample of 80 games

Step-by-step explanation:

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

Normal Probability Distribution:

Problems of normal distributions can be 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 normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean \mu = p and standard deviation s = \sqrt{\frac{p(1-p)}{n}}

The home team therefore wins 50% of its games

This means that p = 0.5

Determine the probability that the home team would win 65% or more of its games in a simple random sample of 80 games

Sample of 80 means that n = 80 and, by the Central Limit Theorem:

\mu = p = 0.65

s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.5*0.5}{80}} = 0.0559

This probability is 1 subtracted by the pvalue of Z when X = 0.65. So

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

By the Central Limit Theorem

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

Z = \frac{0.65 - 0.5}{0.0559}

Z = 2.68

Z = 2.68 has a pvalue of 0.9963

1 - 0.9963 = 0.0037

0.0037 = 0.37% probability that the home team would win 65% or more of its games in a simple random sample of 80 games

7 0
2 years ago
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