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3 July, 03:58

Investment A for $100,000 is invested at a nominal rate of interest, j, convertible semiannually. After 4 years, it accumulates to 214,358.88. (b) Investment B for $100,000 is invested at a nominal rate of discount, k, convertible quarterly. After two years, it accumulates to 232,305.73. 2 (c) Investment C for $100,000 is invested at an annual effective rate of interest equal to j in year one and an annual effective rate of discount equal to k in year two. Calculate the value of investment C at the end of two years.

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  1. 3 July, 04:07
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    Answer: a - 20%

    b - 44.44%

    c - $184423.11

    Explanation: The following could be calculated as follows : -

    (a) Initial Investment = $ 100000,

    Compounding Frequency: Semi-Annual,

    Tenure = 4 years,

    Target Future Value = $ 214358.88

    NOW,

    Therefore, 100000 x [1 + (j/2) ]^ (8) = 214358.88

    solving the equation for J we get : -

    [1 + (j/2) ]^ (8) = 214358.88 / 100000 = 2.1435888

    j/2 = (2.1435888) ^ (1/8) - 1 = 0.1

    j = 20 %

    (b) Initial Investment = $ 100000

    Compounding Frequency: Quarterly,

    Tenure = 2 years pr (4 x 2) = 8 quarters

    Target Future Value = $ 232305.73

    Now,

    100000 x [1 + (k/4) ]^ (8) = 232305.73

    Solving the equation for k we get : -

    [1 + (k/4) ]^ (8) = 232305.73 / 100000 = 2.32305.73

    k/4 = (2.3230573) ^ (1/8) - 1 = 0.1111

    k = 0.4444 or 44.44 %

    (c) Initial Investment = $ 100000

    Annual Effective Interest Rate for Year 1 = (1.1) ^ (2) - 1 = 0.21 or 21 %

    Annual Effective Interest Rate for Year 2 = (1.1111) ^ (4) - 1 = 0.52416 or 52.416 %

    Future Value of Initial Investment = 100000 x (1.21) x (1.52416) = $184423.11
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