My monk has a movement of 50ft and a +4 strength bonus (18 STR). My computation for my maximum jump is start of 10 ft.

I arrive at a high jump of 14 ft + remaining movement which is rounded down of 25 ft + extra movement of dash (step of the wind)=+50ft
Max jump = 89 ft?

Under normal circumstances your high jump would reach 7 ft (3 + your Strength mod of +4).

Certain abilities and spells can increase this, so you would need to give more details on your monk.

Refer to this question

You seem to be under a bit of a misconception on what the jumping rule is actually saying and adding everything up(?). The high jump rule is saying that

1. If you have a run-up of 10ft then your height when jumping is 3 + your Strength mod. This is the number of feet you leap into the air.




2. If you do not have a run-up and just try and leap straight up
   then you only leap half that amount. i.e. 3 + your Strength mod,
   then divide that by two. In your case that would be 3.5 ft




3. The distance you jump is subtracted from the number of feet you can move in a round in order to calculate how much movement you have left. So if you run 10ft then jump forward 7ft, you would still have 33ft of movement left (50ft movement minus the 10ft minus the 7ft jump).

You can High Jump a max 14' with resource expenditure

The jumping rules are detailed in the PHB(p. 182):

When you make a high jump you leap into the air a number of feet equal to 3 + your Strength modifier if you move at least 10 feet on foot immediately before the jump. When you make a standing high jump, you can jump only half that distance. Either way, each foot you clear on the jump costs a foot of movement. (Basic Rules, p. 67)

That gives you a maximum of 7' because you are taking the 10' movement prior to jumping so can add your Strength modifier to the base 3' from jumping.

However, you have the option to spend a Ki Point resource for Step of the Wind. This allows you to (my emphasis):

..spend 1 ki point to take the Disengage or Dash action as a bonus action on your turn, and your jump distance is doubled for the turn.

Jump Distance includes both types of Jumping described: High Jump and Long Jump. It is the distance you could do either action.

This doubles your total jump height to 14'.

Where you went wrong in your calculation

Your mistake was involving your actual movement values(outside of needing 10' to jump your maximum distance) in your calculations for High Jump Distance. The methodology for calculating Jump Distance does not include your movement speed except as a maximum boundary (If you only had a move of 20', you wouldn't be able to jump 14' because you need the initial 10' and only have 10' remaining of total movement.)

High Jump of 14'; movement is reduced by 10' + jump height/length

Your high jump is pretty straight forward: 7' up with a strength of 18 and the monk using a 10' start. A 3.5 foot vertical leap from a standing start. (How far the bottom of your feet are from the ground at the jump's apex).

While "jump distance doubling" seems to fit the long jump and high jump is measured in "height," assume a ruling where height is doubled so you can high jump 14' with a 10' running start, or 7' with a standing start using step of the wind. (I'd rule favorably on doubling the jump height, since cool monk stuff is cool!)
How high can the monk jump? 14' up if Step of the Wind doubles your high jump.

Jumping

Your Strength determines how far you can jump.

High Jump.

When you make a high jump you leap into the air a number of feet equal to 3 + your Strength modifier if you move at least 10 feet on foot immediately before the jump. When you make a standing high jump, you can jump only half that distance. Either way, each foot you clear on the jump costs a foot of movement. (Basic Rules, p. 67)

What happens to the movement with Step of the Wind?

Your question appears to mix jumping and movement.

I arrive at a high jump of 14 ft + remaining movement which is rounded
down of 25 ft + extra movement of dash (step of the wind)=+50ft Max
jump = 89 ft?

You used 14 feet of movement, +10 for the running start. 100 -24 = 76 feet of movement left if you want to use it all.

For a running long jump, 10 feet of movement, cover up to 18' (your strength score, doubled to 36' using SoTW). 100 - 46 equals *54 feet of movement left when using step of the wind and dash* after your maxed out running long jump.

Long Jump

When you make a long jump, you cover a number of feet up to your Strength score if you move at least 10 feet on foot immediately before the jump. When you make a standing long jump, you can leap only half that distance. Either way, each foot you clear on the jump costs a foot of movement. (Basic Rules, p. 67)