How to work back with values using only 1 figure

Lui Cruz said:

Hi,

Am not sure if my problem falls under this category but any help will be appreciated.

I have a table just like below:

Month	Stage 1	Stage 2	Stage 3	Stage 4	Stage 5
Jan-2015					340,542

By merely having one value on Stage 5, so I guess I need to work back to get the value of Stage 1. I have to populate Stages 1-4 of Jan-2015 using the following criteria but I don't know how to do the computation:

1. Values are spread-out from Stages 1-4.
2. There should be an additional 10% from every Stage starting Stage 2 (sample: if Stages 1 and 2 has 100 each, then Stage 2 should have 100+(100*10%).
3. Total value from Stages 1-5 should be 340,542.
4. Same formula should apply for the rest of the months for the same Stages. I did not include Feb-Dec values to save space.

I hope I sound sensible with what I am asking for. Hope you can help me please.

Thanks,

Click to expand...

Ishuda said:

Whether the 10% additional is 10% the first stage or of the last stage isn't said, but I would assume it is of the last stage so let Si be the amount in Stage i and we have

Stage 1: A
Stage 2: A + 0.1 * A
Stage 3: A + 0.1 * (A + 0.1 * A) = A + 0.1 * A + 0.1² * A
Stage 4: A + 0.1 * (A + 0.1 * A + 0.1² * A) = A + 0.1 * A + 0.1² * A + 0.1³ * A
Stage 5: A + 0.1 * (A + 0.1 * A + 0.1² * A + 0.1³ * A) = A + 0.1 * A + 0.1² * A + 0.1³ * A + .01⁴ * A
= A (1 + 0.1 + 0.1² + 0.1³ + .01⁴) = 340542
So what is A?

Click to expand...

Lui Cruz said:

Hi Ishuda,

Unfortunately, I was only given 10% increase and value for Stage 5, so I assumed the only way to get the value is to work back from Stage 5...
Wait, I forgot to tell another criteria:

1. Get the 75% of Stage 5 (meaning 340542 of Stage 5 is only 25% of Stages 1 to 5)
2. This 75% should be spread-out on Stages 1 to 4
3. 10% of Stage 1 should be added to Stage 2 and so on and so forth (up to Stage 5)
4. Having these considerations, the result for Stage 5 should still be 340542.

Click to expand...

Lui Cruz said:

Hi Ishuda,

Unfortunately, I was only given 10% increase and value for Stage 5, so I assumed the only way to get the value is to work back from Stage 5...
Wait, I forgot to tell another criteria:

1. Get the 75% of Stage 5 (meaning 340542 of Stage 5 is only 25% of Stages 1 to 5)
2. This 75% should be spread-out on Stages 1 to 4
3. 10% of Stage 1 should be added to Stage 2 and so on and so forth (up to Stage 5)
4. Having these considerations, the result for Stage 5 should still be 340542.

Click to expand...

Lui Cruz said:

Hi Ishuda,

Unfortunately, I was only given 10% increase and value for Stage 5, so I assumed the only way to get the value is to work back from Stage 5...
Wait, I forgot to tell another criteria:

1. Get the 75% of Stage 5 (meaning 340542 of Stage 5 is only 25% of Stages 1 to 5)
2. This 75% should be spread-out on Stages 1 to 4
3. 10% of Stage 1 should be added to Stage 2 and so on and so forth (up to Stage 5)
4. Having these considerations, the result for Stage 5 should still be 340542.

Click to expand...

Month	Stage 1	Stage 2	Stage 3	Stage 4	Stage 5
Jan-2015					340,542

By merely having one value on Stage 5, so I guess I need to work back to get the value of Stage 1. I have to populate Stages 1-4 of Jan-2015 using the following criteria but I don't know how to do the computation:

1. Values are spread-out from Stages 1-4.
2. There should be an additional 10% from every Stage starting Stage 2 (sample: if Stages 1 and 2 has 100 each, then Stage 2 should have 100+(100*10%).
3. Total value from Stages 1-5 should be 340,542.
4. Same formula should apply for the rest of the months for the same Stages. I did not include Feb-Dec values to save space.

Click to expand...