John is currently 25 years old. He has $10,000 saved up and wishes to deposit this into a savings account which pays him J12 = 6% p. a. He also wishes to
deposit $X every month into that account so that when he retires at 55, he can
withdraw $2000 every month end to support his retirement. He expects to live up till 70 years. How much should he deposit every month into his account?

$832.22

Step-by-step explanation:

John wishes to withdraw $2000 every month when he retires at 55 till he's 70

So there are 70 - 55 = 15 years of withdrawing $2000 monthly.

Amount to be withdrawn in 15 years monthly = $2000*12*15= $360000

So he needs $360000to achieve this goal.

But he is currently 25 and has $10000.

55-25 = 30 years.

6% per annum

A = 10000(1+(0.06/30))^(30*30)

A= 10000(1+0.002)^(900)

A= 10000(1.002)^(900)

A= 10000(6.04)

A= 60400

His savings gave him $60400

But he needs $360000

He still needs

360000-60400= 299600

So how much will he deposit every month for 30 years to give 299600

30*12= 360

He will deposit 360 times.

Then 299600/360= $832.22

He will deposit$ 832.22 every month for 30 years.

< xcy ≅ < xby

step-by-step explanation:

in δcax and δbax,

so, δcax ≅ δbax (side-angle-side or sas)

since δcax ≅ δbax, we can conclude < acx ≅ < abx

in δacy and δaby,

so, δacy ≅ δaby (side-angle-side or sas)

since δacy ≅ δaby, we can conclude < acy ≅ < aby

now,

< acy ≅ < aby

=> < acx + < xcy ≅ < abx + < xby

=> < acx + < xcy ≅ < acx + < xby   (since < acx ≅ < abx already proved above)

subtracting < acx from both sides, we get

< acx + < xcy -< acx ≅ < acx + < xby -< acx

cancelling out < acx and -< acx from both sides, we get

< xcy ≅ < xby (proved)

i am so sorry , i have no idea but i want points so i won't be a beginner anymore