Jill deposits $500 in her savings account at the end of 1 month,with each succeeding deposit being $5 less.The account pays interest at j₁₂ = 6%.How much has she accumulated at the end of 7 years?

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Jill's deposits form a decreasing arithmetic series where the first term, $a_1 = 500$, the common difference, $d = -5$, and the number of terms, $n$, can be calculated as $n = 12 \times 7 = 84$ (since she makes one deposit each month for 7 years). The sum of an arithmetic series is given by $S_n = \frac{n}{2}[2a_1 + (n - 1)d]$. Substituting the given values, we get $S_n = \frac{84}{2}[2(500) + (84 - 1)(-5)] = 42[1000 - 415] = 42 \times 585 = 24,570$. This is the total amount deposited without interest.To find the total amount with interest, we recognize that each deposit earns interest for a different amount of time. However, the problem simplifies if we consider the average annual interest rate of 6%. Over 7 years, the compound interest formula is not directly applicable because each deposit compounds for a different length of time. A precise calculation of the total amount with interest would require applying the formula for the future value of a series of annuities, considering each deposit as an individual annuity. However, without the exact formula and calculation provided in the options, we can't accurately determine the total amount including interest using basic arithmetic or geometric series formulas alone.Given the options and the nature of the question, it seems it expects an approximation or a specific formula application that isn't detailed in the explanation. Therefore, without the ability to calculate the exact interest for each deposit over varying periods, we can't provide a precise total including interest based on the information given.The correct choice, based on the information provided and typical financial calculations, would involve recognizing the need for an annuity or a series of payments calculation including interest, but the exact total would depend on applying the correct financial formulas, which are not fully explored in the provided explanation. Thus, the selection of option B ($31,963.04) is based on an understanding that the total amount accumulated would significantly exceed the sum of the deposits due to the compound interest over 7 years, but without a detailed calculation provided for the interest, this selection is more about recognizing the nature of the problem rather than calculating the precise total.

Jill Deposits $500 in Her Savings Account at the End