## 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.

Find

vn

.

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Math
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2021-09-26T16:26:20+00:00
2021-09-26T16:26:20+00:00 1 Answer
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## Answers ( )

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: