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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Mathematics

Cayden Chavez

3 January, 16:50

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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Jaiden Blackburn · Answer 1

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