A varying annuity has 15 annual payments.The first payment is $2000,and each succeeding payment increases by 5%.What is the accumulated value of these payments immediately after the 15^th deposit if j₁ = 8%? (Answer to nearest dollar)

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The accumulated value of a varying annuity can be calculated using the formula for the future value of a growing annuity. Given the first payment (PMT) is $2000, the growth rate (g) is 5% or 0.05, the interest rate (i) is 8% or 0.08, and the number of payments (n) is 15, the formula for the future value of a growing annuity is:$$ FV = PMT \times \frac{(1 + i)^n - (1 + g)^n}{i - g} $$Plugging in the values:$$ FV = 2000 \times \frac{(1 + 0.08)^{15} - (1 + 0.05)^{15}}{0.08 - 0.05} $$$$ FV \approx 2000 \times \frac{(1.08)^{15} - (1.05)^{15}}{0.03} $$$$ FV \approx 2000 \times \frac{3.1722 - 2.0789}{0.03} $$$$ FV \approx 2000 \times 36441.6667 $$$$ FV \approx 72883 $$Therefore, the accumulated value of these payments immediately after the 15th deposit, rounded to the nearest dollar, is approximately $72,883.

A Varying Annuity Has 15 Annual Payments