Problem

Plans begin together. Plan A deposits $\$100$ at each month-end for $\text{months}~1\text{--}12$. Plan B deposits $\$120$ at each month-end for $\text{months}~1\text{--}10$ and makes $\text{no}~\text{later}~\text{deposits}$. Both use monthly factor $1.005$. Compare immediately after $\text{month}~12$.

Neutral comparison timeline: Plan A deposits $100 at each month-end through month 12; Plan B deposits $120 at each month-end through month 10 and then grows without deposits to the common valuation after month 12. Computed balances and preference are withheld.

Big Picture

What this problem is really about

A fair financial comparison requires one shared valuation date. Accumulate each plan through its own last deposit, then carry any earlier-ending balance forward through the remaining periods even when no new deposits occur. Only after both balances refer to the same instant should they be subtracted and compared.

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Valuing Plan B after month 10 makes Plan A higher by $6.20.

The plans tie because each deposits $1,200.

At month 12, Plan A is preferred although Plan B has $1,239.67 and Plan A has $1,233.56.

At the common valuation after month 12, Plan A has $1,233.56 and Plan B has $1,239.67. Plan B is higher by $6.11.

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