A present-value model treats a whole interest of $980,000 as the sum of a life interest and a remainder, with the life interest at 36% of the whole. There are no transaction costs, interaction effects or other interests. What does this model indicate for the remainder?
Correct Answer
B) $627,200
Life-interest share=$980,000×0.36=$352,800; complementary remainder=$980,000−$352,800=$627,200. Common errors: reporting the life-interest component instead of the remainder gives $352,800; adding the life interest instead of subtracting it gives $1,332,800; reporting the whole interest gives $980,000.
Why This Is the Correct Answer
Option B is correct because the life-interest component is $980,000 x 0.36 = $352,800, and the complementary remainder is $980,000 - $352,800 = $627,200. Under the stated model there are no transaction costs or interaction effects, so the two parts add back to the whole.
Why the Other Options Are Wrong
Option A: $352,800
Option A, $352,800, is the life-interest component itself ($980,000 x 0.36), not the remainder. The remainder is what is left after subtracting that amount: $980,000 - $352,800 = $627,200.
Option C: $980,000
Option C, $980,000, is the value of the whole interest. Reporting it ignores the life-interest share that must be removed; the remainder is $980,000 - $352,800 = $627,200.
Option D: $1,332,800
Option D, $1,332,800, comes from adding the life interest to the whole ($980,000 + $352,800) instead of subtracting it. The correct remainder is $980,000 - $352,800 = $627,200.
Whole minus part equals rest
Find the stated part first, then take it away from the whole to get the complementary part.
How to use: Use this whenever a question gives a whole value and one component and asks for the other component.
Exam Tip
Read the final question carefully: if it asks for the remainder, the percentage result is only an intermediate step, not the answer.
Common Mistakes to Avoid
- -Stopping after computing the 36% share and reporting it as the remainder
- -Adding the life-interest share to the whole instead of subtracting it
- -Assuming real-market partial interests necessarily sum to unencumbered market value
Concept Deep Dive
Analysis
This question tests whether you can split a whole interest into two complementary parts under a stated additive model. The life-interest share is given as a percentage of the whole, so you first compute that share and then subtract it from the whole to find the remainder.
Background Knowledge
Ownership of real property can be divided into components such as life estates and remainders, or leased fee and leasehold interests. In an additive model the components sum to the whole, but in real markets separately marketable partial interests do not necessarily add to unencumbered market value.
Real-World Application
An appraiser is asked to illustrate how a $980,000 property might be allocated between a life tenant and a remainderperson under an agreed additive model. The appraiser computes the life share and reports the remainder as the difference, while noting that actual market values of partial interests may not sum to the whole.
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