A commercial building sold for $1,000,000 two years ago and recently sold for $1,115,000. What is the adjustment for time per month using the compounding method?

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Multiple Choice

A commercial building sold for $1,000,000 two years ago and recently sold for $1,115,000. What is the adjustment for time per month using the compounding method?

Explanation:
Time adjustments in this method treat market changes as a growth process that compounds monthly. The two-year period saw a price rise from 1,000,000 to 1,115,000, a total factor of 1.115 over 24 months. To find the monthly compounding rate, solve (1 + r)^{24} = 1.115. Taking natural logs gives r = exp(ln(1.115)/24) − 1. Numerically, ln(1.115) ≈ 0.1098; dividing by 24 gives ≈ 0.00458; exponentiating and subtracting 1 yields r ≈ 0.00459, or about 0.459% per month. This aligns with 0.455% per month as the closest option.

Time adjustments in this method treat market changes as a growth process that compounds monthly. The two-year period saw a price rise from 1,000,000 to 1,115,000, a total factor of 1.115 over 24 months. To find the monthly compounding rate, solve (1 + r)^{24} = 1.115. Taking natural logs gives r = exp(ln(1.115)/24) − 1. Numerically, ln(1.115) ≈ 0.1098; dividing by 24 gives ≈ 0.00458; exponentiating and subtracting 1 yields r ≈ 0.00459, or about 0.459% per month. This aligns with 0.455% per month as the closest option.

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