To solve this problem, we will apply the concept of geometric progression (GP), since the land’s value increases by a fixed percentage (5%) each year.

The formula for the $n$-th term of a geometric sequence is:

$A_n = A_1 \times (1 + r)^{n-1}$

where:

• $A_n$ is the value of the land after $n$ years,
• $A_1$ is the initial value of the land,
• $r$ is the rate of appreciation (expressed as a decimal), and
• $n$ is the number of years.

Step 1: Determine the known values

• Initial value ($A_1$) = ₦50,000
• Rate of appreciation ($r$) = 5% = 0.05
• Time period to forecast is 10 years (since 5 years have already passed, and we want the value after another 5 years).

Step 2: Calculate the value of the land after 10 years

We need to apply the formula for the value after 10 years:

$A_{10} = 50,000 \times (1 + 0.05)^{10}$ $A_{10} = 50,000 \times (1.05)^{10}$ $A_{10} = 50,000 \times 1.62889463$ $A_{10} \approx 81,444.73$

Conclusion:

The value of the land in another 5 years (after 10 years in total) will be approximately ₦81,444.73.

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Would you like to dive deeper into the derivation of this formula, or do you have any questions about this approach?

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Related Questions:

1. How do I calculate the future value of a sum of money using compound interest formulas?
2. How does the number of years affect the growth of a value in a geometric progression?
3. What would happen if the rate of appreciation were to change over time, rather than staying fixed at 5%?
4. How can I calculate the present value of an investment given a future value and interest rate?
5. What are some real-life applications of geometric progressions in finance?

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Tip: In finance, geometric progressions are often used to model investment growth, like in stocks or real estate. Always check if the growth is compounded annually, as this simplifies using the formula directly.