An investor deposits P dollars on the first day of each month in an account with an

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An investor deposits P dollars on the first day of each month in an account with an annual interest rate r, compounded monthly. The balance A after t years is
A = P (1 + r / 12) + . . . + P (1 + r / 12)12t.
Show that the balance is
A = P [(1 + r / 12)12t - 1] (1 + 12 / r).
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