## 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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Math
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2021-12-30T23:10:49+00:00
2021-12-30T23:10:49+00:00 1 Answer
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## Answers ( )

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*sqrt(0.5)*0.25

PV = 1414.213562