At an effective annual interest rate i, i > 0, each of the following two sets of payments has present value K: a. A payment

Question

At an effective annual interest rate i, i > 0, each of the following two sets of payments has present value K:

a. A payment of 121 immediately and another payment of 121 at the end of one year
b. A payment of 144 at the end of two years and another payment of 144 at the end of three vears.

Calculate i.

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RI SƠ 5 years 2021-08-30T03:46:53+00:00 1 Answers 114 views 0

Answers ( )

  1. kimchi2
    0
    2021-08-30T03:48:26+00:00
    Reply

    Answer:

    Hence the calculated

    Step-by-step explanation:

    Now,

    121+121v=144v^{2} + 144 v^{3} =K\\121(1+v)=144v^{2} (1+v)\\v^{2} =\frac{121}{144} \\\\v=\frac{11}{12}

    Then K is calculated as,

    K=121(1+v)\\K=121(1+\frac{11}{12} )\\K=\frac{121(23)}{12} \\\\K= 231.916

    Here we get,

    i=\left | \left ( \frac{v-1}{v} \right ) \right |\\i=\left | \frac{\frac{11}{12}-1}{\frac{11}{12}} \right |\\i=\frac{1}{11}

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