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34kurt
3 years ago
8

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

ts 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
.
Mathematics
1 answer:
vladimir1956 [14]3 years ago
6 0

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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Now multiply the common terms into inside the bracket.

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$h\left(\frac{15}{32} \right)=10.02

Hence the value of h(t) when t=\frac{15}{32} is 10.02.

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