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3 years ago

How much money would you need to deposit today at 7% annual interest

Mathematics

1 answer:

Monica [59]3 years ago

4 0

Answer:

$33,090.

Step-by-step explanation:

The formula is A = P( 1 + r/2)^2n so we have:

50,000 = P(1 + 0.07/2)^(6*2)

50000 = P * 1.035^12

P = 50000/ 1.035^12

= $33,090 to the nearest dollar.

You might be interested in

1. Alice invests $1000 at 2% interest compounded monthly over a 5 year period. Assuming no other money is deposited or withdrawn

eduard

Answer:

$1,105.08.

Step-by-step explanation:

Given that Alice invests $ 1000 at 2% interest compounded monthly over a 5 year period, assuming no other money is deposited or withdrawn, to determine what is the total amount of money in her account after 5 years, the following calculation must be performed:

X = 1,000 (1 + 0.02 / 12) ^ 5x12

X = 1,105.08

Thus, the amount of money in her account after 5 years would be $ 1,105.08.

6 0

3 years ago

The diameters of bolts produced in a machine shop are normally distributed with a mean of 5.18 millimeters and a standard deviat

dimulka [17.4K]

As per the concept of normal distribution, the two diameters of the bolt that has separate the top 3% and the bottom 3% are 5.2836 mm and 5.0764 mm respectively .

Normal distribution:

Normal distribution means the probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean and it has the bell shaped curve.

Given,

The diameters of bolts produced in a machine shop are normally distributed with a mean of 5.18 millimeters and a standard deviation of 0.07 millimeters.

Here we need to find the two diameters that separate the top 3% and the bottom 3% and these diameters could serve as limits used to identify which bolts should be rejected. we have also round off the result into nearest hundredth.

Here we have the given question with the values of,

The value of Mean is 5.18 millimeters

The value of Standard deviation is 0.07 millimeters.

Here we have to consider the following two cases, they are.

Case 1

We need to find x₁ such that that is P(X > x₁) = 3% when we convert it into decimal then we get P (X > x₁) = 0.03

So, as per the probability,

P (X ≤ x₁) = 1 - 0.03 = 0.97

So, z corresponding to the value of p = 0.97 is 1.48

Apply the given values to the formula of normal distribution then we get,

=> 1.48 = (x₁ - 5.18) /0.07

=> 0.1036 = x₁ - 5.18

Therefore, the value of x₁ is 5.2836

So, the diameter of the both with separate top 3% is 5.2836.

Case 2:

Next we have to take P(X < x₂) = 3% when we convert it into decimal then we get P (X < x₂) = 0.03

So, as per the given probability, the value of

P (X ≤ x₂) = 1 - 0.03 = 0.97

So, z corresponding to but here we have to use the negative because of the less than concept p = 0.97 is -1.48

Apply the values on the formula of normal distribution then we get,

-1.48 = (x₂ - 5.18) /0.07

Move the value to the other side

-0.1036 = x₂ - 5.18

When we simplify it,

x₂ = 5.0764

So, the diameter of the both with separate bottom 3% is 5.0764

To know more about Normal distribution here.

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7 0

1 year ago

The grocery store sells kumquats for $5.00 a pound and Asian pears for $3.25 a pound. Write an equation in standard form for the

Lilit [14]

I can simplify the formula with the data you gave me to do a simple formula like this: 4.25 k + 2 p = 12 I think this one explains in an easy way this. Hope it's good for you

8 0

3 years ago

Do many fishermen collect worms at night?

stealth61 [152]

The question actually relates to finding the direct object in the sentences given.
In the first sentence, the direct object is "worms". The correct option among all the options that are given in the question is the third option or option "C".

In the second sentence, the direct object is "worms". The correct option among all the options that are given in the question is the first option or option "A".

In the third sentence, the direct object is "worms". The correct option among all the options that are given in the question is the third option or option "C".

6 0

3 years ago

A random sample of 102 full-grown lobsters had a mean weight of 16 ounces and a standard deviation of 3.4 ounces. Construct a 98

pshichka [43]

Answer:

The best point estimate for a confidence interval estimating the population μ is 16 ounces.

The 98 percent confidence interval for the population mean μ is between 15.21 ounces and 16.79 ounces.

Step-by-step explanation:

We have the standard deviation for the sample, so we use the t-distribution to solve this question.

The best point estimate for a confidence interval estimating the population μ is

The sample mean, so 16 ounces.

T interval

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 102 - 1 = 101

98% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 101 degrees of freedom(y-axis) and a confidence level of $1 - \frac{1 - 0.98}{2} = 0.99$ . So we have T = 2.36

The margin of error is:

$M = T\frac{s}{\sqrt{n}} = 2.36\frac{3.4}{\sqrt{102}} = 0.79$

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 16 - 0.79 = 15.21 ounces

The upper end of the interval is the sample mean added to M. So it is 16 + 0.79 = 16.79 ounces

The 98 percent confidence interval for the population mean μ is between 15.21 ounces and 16.79 ounces.

4 0

2 years ago