Tracy recieves payments of $X at the end of each year for n years. The present value of her annuity is 493. Gary receives payments on $3X at

Question

Tracy recieves payments of $X at the end of each year for n years. The present value of her annuity is 493. Gary receives payments on $3X at the end of each year for 2n years. The present value of his annuity is $2,748. Both present values of calculated wit the same annual effective interest rate.

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vn
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Jasmine 3 weeks 2021-09-26T16:26:20+00:00 1 Answer 0

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    2021-09-26T16:27:58+00:00

    Answer:

    v = 1/(1+i)

    PV(T) = x(v + v^2 + … + v^n) = x(1 – v^n)/i = 493

    PV(G) = 3x[v + v^2 + … + v^(2n)] = 3x[1 – v^(2n)]/i = 2748

    PV(G)/PV(T) = 2748/493

    {3x[1 – v^(2n)]/i}/{x(1 – v^n)/i} = 2748/493

    3[1-v^(2n)]/(1-v^n) = 2748/493

    Since v^(2n) = (v^n)^2 then 1 – v^(2n) = (1 – v^n)(1 + v^n)

    3(1 + v^n) = 2748/493

    1 + v^n = 2748/1479

    v^n = 1269/1479 ~ 0.858

    Step-by-step explanation:

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