A plot of land is valued at R312,358. If it increases in value at a rate of 10.3% per annum (compounded annually), what is the value at the end of 7 years?

To determine the future value of the plot of land, we use the formula for compound interest:

\[ A = P \left(1 + \frac{r}{100}\right)^n \]

where:
- \( A \) is the amount of money accumulated after \( n \) years, including interest.
- \( P \) is the principal amount (the initial value of the plot of land).
- \( r \) is the annual interest rate (as a percentage).
- \( n \) is the number of years.

Given:
- \( P = \text{R}312,358 \)
- \( r = 10.3\% \)
- \( n = 7 \)

Let's plug these values into the formula:

\[ A = 312,358 \left(1 + \frac{10.3}{100}\right)^7 \]
\[ A = 312,358 \left(1 + 0.103\right)^7 \]
\[ A = 312,358 \left(1.103\right)^7 \]

Now, we calculate \( (1.103)^7 \):

\[ (1.103)^7 \approx 2.002 \]

So, the future value \( A \) is:

\[ A = 312,358 \times 2.002 \]
\[ A \approx 625,376.516 \]

Therefore, the value of the plot of land at the end of 7 years will be approximately \(\text{R}625,376.52\).

Would you like more details or have any questions?

Here are some related questions you might find interesting:
1. How would the value change if the interest rate were 12% instead?
2. What would be the value at the end of 10 years with the same interest rate?
3. How much would the plot be worth if the interest was compounded semi-annually instead?
4. How do you calculate the rate of return if you know the initial and final values?
5. What is the formula for continuous compounding interest?
6. How does the interest rate impact the doubling time of an investment?
7. How does the frequency of compounding affect the future value of an investment?
8. What is the difference between nominal and effective interest rates?

**Tip:** When dealing with compound interest, remember that the frequency of compounding can significantly impact the final amount. The more frequent the compounding, the higher the future value will be.

Learn how to calculate the future value of an investment using compound interest. Solve a problem involving a plot of land valued at R312,358, increasing at a rate of 10.3% per annum over 7 years. Discover the impact of compound interest on investments.

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