At an annual effective interest rate of i, the following are all equal: i) the present value of 10,000 at the end of 6 years i

Question

At an annual effective interest rate of i, the following are all equal:
i) the present value of 10,000 at the end of 6 years
ii) the sum of the present values of 6,000 at the end of the year t and 56,000 at the end of the 2t; and
iii) 5,000 immediately
calculate the present value of a payment of 8,000 at the end of year t+3 using the same annual effective interest rate.

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Adalyn 3 weeks 2021-12-30T23:10:49+00:00 1 Answer 0 views 0

Answers ( )

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    2021-12-30T23:12:07+00:00

    Answer:

     PV = 1414.213562

    Step-by-step explanation:

    Find:

                                  PV = 8,000*V^(t+3)

    Solution:

    Split the the exponent of V into t and 3:

                                   PV = 8,000*V^t*V^3

    – We will calculate the V^t and V^3 from information given.

    – The present value of 10,000 at the end of 6 years and immediate value of $5,000. De-crypt this statement we have:

                                  10,000*V^6 = 5,000

                                   V^6 = 5,000/10,000

                                    V^6 = 0.5

                                    V^3 = sqrt(0.5)

    – Using 2 and 3, De-crypt:

                                  6000*V^t + 56,000*V^2t = 5000

    Solving the quadratic in V^t:

                                   V^t = 0.25

    Hence, we have the present value as:

                                    PV = 8,000*V^t*V^3

                                    PV = 8,000*sqrt(0.5)*0.25

                                   PV = 1414.213562

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