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If you want to retire in 25 years, draw $50,000 each year forever, with an APR of 7%, how much do you need to deposit every month?

To draw $50,000 out at the end of each year for ever than it will only be the interest that your are drawing out.

I=PRT

50000=P*0.07*1

50000/0.07 =  approx $714 286

Plus I suppose you will want to draw out 50,000 straight away so you will need to save    $764 286.

Now I will assume that the 7% is a nominal annual rate.

The real rate for depositis is    7/12 = 0.58333333... %  per month and this will go one for 25*12 = 300months.

I will assume that the deposit is made at the end of each month (even the very last month)

764286=C*((1.0058333333333)^300-1)/0.00583333333333

C= 764286/(((1.0058333333333)^300-1)/0.0058333333333)

764286/(((1.0058333333333)^300-1)/0.0058333333333) = 943.4794556918817245

It seems that you will need to save $944 per month.  

Since 256  =  2⁸  and  sqrt(2)  =  2^1/2:

   256·sqrt(2)  =  2⁸·2^1/2  =  2^{8 + 1/2}  =  2^17/2  (when multiplying numbers with the same base, add                                                                                  the exponents)

sqrt(2)¹⁷  =  (2^1/2)¹⁷  =  2^17/2

Therefore:  256·sqrt(2)  =  sqrt(2)¹⁷  because both equal  2^17/2.

Is there a mistake in the problem?

Did you mean for the second equation to be:  -10 - 7y  =  -24

                                                              --->                  - 7y  =  -14

                                                                                           y  =  2

Then:  -3x - 7y  =  -66

          -3x -7(2)  =  -66

            -3x - 14  =  -66

                   -3x  =  -52

                       x  =  17 1/3

Solve for x:
(9 log(x))/(log(10)) = 2

Divide both sides by 9/(log(10)):
log(x) = (2 log(10))/9

(2 log(10))/9 = log(10^(2/9)):
log(x) = log(10^(2/9))

Cancel logarithms by taking exp of both sides:
Answer: |x = 10^(2/9)=1.6681

90min  BRUH

Tau.

It's just the digits of Pi, doubled. No one is actually going to answer that question for you.

It's great to use if you're using radians for graphing maths.

9 + 9 = 18

🤗

i get that to

=-1/3+7/4

=-4/12+21/12

=17/12

=1 and 5/12

1/15  =  0.06666666666666666...

1.06666666666666666...  =  1 1/15  =  16/15

What is 1.0666666666666667 as an improper fraction?

=1 1/15 =16/15

8 times 100 plus  3 times 1/10 plus 6 times 1/100

 [8 * 100 ]  + [ 3 * (1/10)]   +  [ 6 * (1/100)]  =

800 + 3/10  + 6/100  =

800.36

3(1/3) + (-7/4)  =

1  - 7/4   =

4/4  - 7/4  =

-3/4

3(13) + (-7/4)  =

39  - 7/4   =

156/4 - 7/4  = 

[156 - 7]  / 4  =

149/4

 x+3y-3z=-12      (1)

3x-3y-4z=14       (2)

-5x+4y+5z=-15    (3)

Add (1)  and (2)

4x - 7z   = 2     (4)

Multiply (1) by 4   and (3)  by -3....this gives us

4x + 12y - 12z = -48

15x - 12y - 15z = 45        add these giving us

19x - 27z   = -3     (5)      multiplly (4) by 19   and (5)  by -4   ....this gives us.....

76x - 133z = 38

-76x + 108z = 12        add these

-25z   = 50       divide both sides by -25

z =  - 2    and using (4)  to find x, we have  that  4x - 7(-2)  = 2  →    4x + 14  = 2   →  4x = -12 →   x = -3

And using (1) to find y, we have :  -3 +3y-3(-2)=-12 →   3 + 3y  = -12   →  3y = -15  →  y  = -5

0 x+19 y-10 z = -75 | (equation 2)
0 x+0 y+z = -2 | (equation 3)
Add 10 × (equation 3) to equation 2:
{-(5 x)+4 y+5 z = -15 | (equation 1)
0 x+19 y+0 z = -95 | (equation 2)
0 x+0 y+z = -2 | (equation 3)
Divide equation 2 by 19:
{-(5 x)+4 y+5 z = -15 | (equation 1)
0 x+y+0 z = -5 | (equation 2)
0 x+0 y+z = -2 | (equation 3)
Subtract 4 × (equation 2) from equation 1:
{-(5 x)+0 y+5 z = 5 | (equation 1)
0 x+y+0 z = -5 | (equation 2)
0 x+0 y+z = -2 | (equation 3)
Subtract 5 × (equation 3) from equation 1:
{-(5 x)+0 y+0 z = 15 | (equation 1)
0 x+y+0 z = -5 | (equation 2)
0 x+0 y+z = -2 | (equation 3)
Divide equation 1 by -5:
{x+0 y+0 z = -3 | (equation 1)
0 x+y+0 z = -5 | (equation 2)
0 x+0 y+z = -2 | (equation 3)
Collect results:
Answer: |x = -3                 y = -5                z = -2

25^221 =8.8052545x 10^308. This is very small number!!!.

-9504

Your Welcome!

cos (59)   =  8 / hypotenuse   .......  rearrange as

hypotenuse = 8 / cos (59)   ≈   15.53

_nP₂  =  n! / (n - 2)!  =  [ n·(n-1)·(n - 2)·(n - 3)·...·1 ] / [ (n - 2)·(n - 3)·...·1 ]  = n·(n - 1)

Since  _nP₂  =  30   --->   n·(n - 1)  =  30

                                             n² - n  =  30

                                      n² - n - 30  =  0

                                  (n - 6)(n + 5)  =  0

                    Either:  n = 6  or  n = -5

Since  n = -5 is impossible (by definition),  n = 6.

e ≈  2.71828

2^√2 ≈  2.665

On the calculator? because 25^221 is nowhere near infinity. Infinity isn't a number, it's a concept of a never-ending number.