Final answer:
The approximate value of the land 61 years later in 2021, after an annual increase of about 5%, would be approximately $560,383.93, which is not an exact match to any of the options provided. The calculation is based on the compound interest formula with an initial amount of $30,000.
Step-by-step explanation:
To calculate the approximate value of the land 61 years later in 2021 after an annual increase of about 5%, we would use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
- A is the amount of money accumulated after n years, including interest.
- P is the principal amount (the initial amount of money).
- r is the annual interest rate (decimal).
- n is the number of times that interest is compounded per year.
- t is the time the money is invested or borrowed for, in years.
In our case, since the interest is compounded once per year (annually), the formula simplifies to:
A = P(1 + r)^t
Using P = $30,000, r = 0.05 (5%), and t = 61 years, we get:
A = $30,000(1 + 0.05)^61
A ≈ $30,000(1.05)^61
A ≈ $30,000(18.67946435)
A ≈ $560,383.93
This means the approximate value of the land in 2021 after 61 years would be about $560,383.93. Hence, none of the options A, B, or C is accurate. The correct answer is closest to option B but not exactly the same.