Could someone explain to me why I divide by 1.05 instead of subtract 5%?

[cdanj]

Here is the question:
An upgraded house in a subdivision recently sold for $210,000. The subject is a similar house but has no upgrades. The sold property is judged to be 5% superior to the subject property. What is the value indicated for the subject property by this sale?
Seems like I should just multiple by 5% and negatively adjust that amount down.
NO!!
CORRECT ANSWER: $200,000

YOUR ANSWER: $199,500

RATIONALE

Mathematically, this would be calculated as $210,000 / 1.05.

Could someone explain to me why I should divide by 1.05 instead of subtract 5%?

I just don't get it.

 

[Terrel L. Shields]

199,500 x 1.05 = 209,475 - so yes, you need to divide by 1.05 - it is 5% superior

 

[Elliott]

This is what Bing AI says:

 

[TerryRohrer]

The 5% is relative to the value of the subject, not the sale. Easiest to write the formula:

1.05*Subject Value = $210,000
Subject Value = $210,000/1.05 = $200,000

 

[Zephyr999]

It's math equations...as @TerryRsays...best to know backwards and forwards.

10% up is NOT the same as 10% down

 

[Overimprovement]

Its the same concept as recouping a loss in the market. If your portfolio loses 10%, it will take MORE than a 10% gain to get back to where you started.
Its also the difference in compound vs simple interest--different way to think about it.

 

[RCA]

Its the same concept as recouping a loss in the market. If your portfolio loses 10%, it will take MORE than a 10% gain to get back to where you started.
Its also the difference in compound vs simple interest--different way to think about it.

When you calculate 10% loss on X, that means your basis for calculation is X. When you calculate what it will take to regain that original value from the new value, the basis for calculation is 0.90X. So because you have different bases, you will have different bases adjustments, So, a 10% loss to X, and a 11.11% gain to 0.9x

0.90X * 1.11 = 1.0

 

[Amy Perkins]

Here is the question:
An upgraded house in a subdivision recently sold for $210,000. The subject is a similar house but has no upgrades. The sold property is judged to be 5% superior to the subject property. What is the value indicated for the subject property by this sale?
Seems like I should just multiple by 5% and negatively adjust that amount down.
NO!!
CORRECT ANSWER: $200,000

YOUR ANSWER: $199,500

RATIONALE

Mathematically, this would be calculated as $210,000 / 1.05.

Could someone explain to me why I should divide by 1.05 instead of subtract 5%?

I just don't get it.

Because 5% of 100k is 5,000 x2 is 10k so it's 5% of 200k not 5% less of 210k. The question is phased so it's 5% less of the missing figure. Say x is the missing amount it's 5% of x not 5% of 210k.

 

[Elliott]

The real trick is in explaining and supporting how you came up with the '5% better.'

 

[cdanj]

The real trick is in explaining and supporting how you came up with the '5% better.'

I'm just trying to figure out a way to remember how to answer a question on a test correctly.