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.

 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

(-5,-28)

i graphed to on desmos.