Suppose that we observe two comparable properties that have each sold twice within the past four years. Property A sold 24 months ago for $500,000 and Property B sold 48 months ago for $575,000. If the two properties were sold today at $425,000 and $465,000, respectively, estimate the change in market conditions (percentage change in price) per month, assuming we equally weight the two properties in our analysis.

0.475% per month

Explanation:

value of property A 24 months ago = $500,000

current value of property A = $425,000

total decrease in value = $500,000 - $425,000 = $75,000 or 15%

monthly % decrease:

1.15 = (1 + r)²⁴

²⁴√1.15 = (1 + r)

1.0058 = 1 + r

r = 0.00584 = 0.58% decrease per month

value of property B 48 months ago = $575,000

current value of property A = $465,000

total decrease in value = $575,000 - $465,000 = $110,000 or 19.13%

monthly % decrease:

1.1913= (1 + r)⁴⁸

⁴⁸√1.1913 = (1 + r)

1.0037 = 1 + r

r = 0.0037 = 0.37% decrease per month

if both properties are weighted equally, then the market decrease per month = (0.58% x 1/2) + (0.37% x 1/2) = 0.475% per month

the investment was $14,174.196

explanation:

a lump sum means that the father of the example made one deposit and leave it be.

we need to know the value of a capital that generated at 4.05% per year during 28 years the sum of $48,613.24

now clearing the formula to solve for capital we got:

and we reach the answer investment = $14,174.20

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