Problem

Find the account balance immediately after the $\text{fourth}$ $\$500$ year-end contribution at annual growth factor $1.06$. State the growth exponents, included contributions, geometric series and formula, and approximate balance.

Neutral cash-flow timeline showing four equal positive $500 end-of-year contributions, valued immediately after contribution 4; growth exponents, series formula, and balance are withheld.

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Growth exponents: 3 through 1. Contributions included: first 3; final contribution omitted. Series/formula: 500[(1.06)³+…+1.06]. Balance: about $1687.31.

Growth exponents: 4 through 1. Contributions included: all 4, each one year too long. Series/formula: 500·1.06[(1.06)³+…+1]. Balance: about $2318.55.

Growth exponents: 3 through 0. Contributions included: all 4. Series/formula: 500[(1.06)³+…+1]=500((1.06)⁴-1)/0.06. Balance: about $2187.31.

Growth exponents: 3 for every contribution. Contributions included: all 4. Series/formula: 4·500(1.06)³. Balance: about $2382.03.

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Find the account balance immediately after the \(\text{fourth}\) \(\$500\) year-end contribution at annual growth factor \(1.06\). State the growth exponents, included contributions, geometric series and formula, and approximate balance.

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