Answer:
$83,802
Explanation:
The description is of an annuity due. Payments at the beginning of the period earn interest for the period, unlike those made at the end of the period.
Formula
The future value of an annuity due is given by the formula ...
FV = P(1 +r)((1 +r)^t -1)/r
where P is the annual payment, r is the annual interest rate, and t is the number of years.
This is essentially the sum of t terms of a geometric series with first term P(1+r) and common ratio (1+r).
Application
For P=$1000, r = 0.06, and t = 30, the future value is ...
FV = $1000(1.06)(1.06^30 -1)/0.06 ≈ $83,801.68
To the nearest dollar, the account value will be $83,802.
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Additional comment
Spreadsheets and many graphing calculators have time-value-of-money (TVM) formulas built in. You need to make sure to choose the option that gives an annuity due, rather than an ordinary annuity. In the attached TVM picture, this setting is accomplished by PmtMode=1.