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Calculate the future value of K50,000 after 2 years at an 8% annual appreciation rate, and evaluate K2,000 at a 10% annual depreciation rate for 3 years.

Mathematics

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Step-by-step solution

6 steps

:

  1. Identify the initial cost, appreciation rate, and time.

    The initial cost (principal) is P=K50 000P = \text{K}50\,000.
    The appreciation rate is r=8%=0.08r = 8\% = 0.08.
    The time period is n=2n = 2 years.

  2. Use the compound appreciation formula A=P(1+r)nA = P(1 + r)^n.

    A=K50 000(1+0.08)2A = \text{K}50\,000 (1 + 0.08)^2

  3. Calculate the value after 2 years.

    A=K50 000(1.08)2A = \text{K}50\,000 (1.08)^2 A=K50 000(1.1664)A = \text{K}50\,000 (1.1664) A=K58 320A = \text{K}58\,320

    The land would cost K58 320 after 2 years.

    :

  4. Simplify the expression inside the parenthesis.

    K2 000(1−10%)3K2\,000 (1 - 10\%)^3 K2 000(1−0.10)3K2\,000 (1 - 0.10)^3 K2 000(0.90)3K2\,000 (0.90)^3

  5. Calculate the cube of 0.90.

    K2 000(0.729)K2\,000 (0.729)

  6. Multiply the result by K2 000.

    K2 000×0.729=K1 458K2\,000 \times 0.729 = K1\,458

    The evaluated value is K1 458.

    :
    The exchange rate for AU$ 1.00 is missing from the question. Please provide the exchange rate to complete this problem.

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