Land is worth 381,620,000 baht on 2 September 2024 and its price grows 4% per year. What will it be worth on 1 January 2025?

Step-by-step solution

1. 1

   Count the days between the two dates exactly. From 2 September to 30 September is $28$ days, then October $31$, November $30$ and December $31$, and one more day to reach 1 January: $28 + 31 + 30 + 31 + 1 = 121$ days. Guessing "about four months" would already cost several hundred thousand baht.

2. 2

   Express the holding period as a fraction of a year.

   $t = \frac{121}{365} = 0.331507\ \text{years}$

3. 3

   Use the compound-growth formula with a fractional exponent. A rate quoted "per year" compounds continuously across the year, so the growth factor over a partial year is $(1+r)^t$, not $1 + rt$:

   $V = P(1+r)^t = 381{,}620{,}000\,(1.04)^{121/365}$

4. 4

   Evaluate the growth factor to full precision.

   $(1.04)^{0.331507} = e^{0.331507 \ln 1.04} = e^{0.0130018} = 1.01308683$

   Rounding this factor to $1.0131$ before multiplying is the step where accuracy is usually lost.

5. 5

   Multiply and report.

   $V = 381{,}620{,}000 \times 1.01308683 = 386{,}614{,}195\ \text{baht}$

   The gain is about $4.99$ million baht, roughly one third of a full year's $4\%$ growth ($15.26$ million) — consistent with $t \approx 0.33$.

6. 6

   Note the effect of the premature rounding. Using the four-decimal factor $1.0131$ instead gives $386{,}618{,}622$ baht, about $4{,}400$ baht too high. Carry the factor to at least eight significant figures when the principal runs into the hundreds of millions.