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Talja [164]
1 year ago
15

gary has just retired, and has 750000 dollars in his retirement account. the account will earn interest at an annual rate of 5 p

ercent, compounded monthly. at the end of each month, gary will withdraw a fixed amount to cover his living expenses. gary wants his savings to last 30 years. how much money can he withdraw each month
Mathematics
1 answer:
ch4aika [34]1 year ago
7 0

The amount of money that Gary can withdraw each month is equal to $4026.18.

<u>Given the following data:</u>

  • Value of each payment, P = 750,000 dollars.
  • Annual percentage interest rate, APR = 5% = 0.05.
  • Time, t = 30 years.

<h3>What is APR?</h3>

APR is an acronym for annual percentage rate and it can be defined as a measure of an amount of money based on a yearly rate of interest, which a borrower must pay on a loan or credit card.

This ultimately implies that, the annual percentage rate (APR) would be calculated by dividing the rate of interest by twelve (12).

Rate of interest, r = APR/12

Rate of interest, r = 0.05/12

Rate of interest, r = 0.0041667

Next, we would calculate the present value of this ordinary annuity by using this formula:

Present value, PV = [P ÷ [1 - (1 + r)^{-nt}]/r]

Substituting the given parameters into the formula, we have;

Present value = [750,000 ÷ [(1 - (1 + 0.0041667)^{-30 × 12})/0.0041667]

Present value = [750,000 ÷ [(1 - (1.0041667)^{-360})/0.0041667]

Present value = [750,000 ÷ [(1 - 0.2238239)/0.0041667]

Present value = [750,000 ÷ [0.7761761/0.0041667]

Present value = 750,000 ÷ 186.280773754

Present value, PV = $4026.18.

Read more on present value on annuity here: brainly.com/question/13373662

#SPJ1

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The roosevelt middle school band is having a fundraiser. They sold a total of 300 hotdogs and hamburgers. Hot dogs were sold for
STALIN [3.7K]

Answer:

180 hamburgers

120 hotdogs

Step-by-step explanation:

In this question, we are asked to calculate the number of hamburgers and hotdogs sold by a company given the amount made by them and the total number of these snacks sold

We proceed as follows;

Let the amount of hotdogs sold be x and the amount of hamburgers sold be y.

We have a total of 300 snacks sold, mathematically;

x + y = 300 ..........(I)

Now let’s look at the prices.

x number of hotdogs sold at $2, this give a total of $2x hotdogs

y number of hamburgers sold at $3, this give a total of $3y.

Adding both to give total, we have ;

2x + 3y = 780.......(ii)

This means we have two equations to solve simultaneously. From equation 1, we can say x = 300 -y

Now let’s insert this in the second equation;

2(300-y) + 3y = 780

600-2y + 3y = 780

y = 780-600 = 180

Recall; x + y = 300

x = 300 -y

x = 300-180 = 120

5 0
3 years ago
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KiRa [710]

Answer: It would be B

Step-by-step explanation:

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3 years ago
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Korvikt [17]
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True or false: sec^-1(0.5) is undefined. explain your answer
ICE Princess25 [194]

Here we get the statement:

"sec^-1(0.5) is undefined"

And we want to see if this is true or false, so let's use the properties that we know to find that this is false.

Remember that the sec function is defined as:

sec(x) = \frac{1}{cos(x)}

Then we will have:

sec^{-1}(x) = (\frac{1}{cos(x)})^{-1} =  cos(x)

Then is really trivial to see that:

sec^{-1}(0.5) =  cos(0.5) = 0.878

Then we can conclude that the function is not undefined at 0.5, so the statement is false.

Below you can see the graph of the given function, and you will see that it is never undefined.

If you want to learn more, you can read:

brainly.com/question/16453813

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3 years ago
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The difference between two numbers is 7. The sum of twice the larger number and three times the smaller number is 19.
Alex17521 [72]

Answer:

x= 8   y= 1

Step-by-step explanation:

First, you identify your variables:

x= larger number

y= smaller number

Second, you find your equations:

x - y = 7

2x + 3y = 19

Third, (I used the substitution method) you make "y" by itself for the 1st equation.

y = x - 7

2x + 3y = 19

Then, you plug in the 1st equation for "y" in the 2nd equation

2x + 3(x - 7) = 19

Then, you distribute and simplify.

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Finally, you plug in the variable you found ( x ) into one of the equations and solve,

8 - y = 7

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y = 1

6 0
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