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Use one side of the transaction
For an investor, a contribution is an outflow and a withdrawal or final liquidation is an inflow. The account ledger can show the opposite perspective. Choose one perspective before solving a rate; mixing signs can remove or create a root.
Keep dated transfers in the equation
An original equally spaced schedule is −100 at time zero, −100 at year one and +242 at year two. The equation is −100−100/(1+r)+242/(1+r)² = 0. The second contribution is funded for only one year.
Check the rate by reconstructing amounts
At r = 10%, the first contribution grows to 121 and the second to 110 at year two, totaling 231 rather than 242. The correct positive-domain root in this case is approximately 13.401346%. Verify the root against the complete schedule instead of averaging capital balances.
State how dates are handled
This example uses exact annual intervals. Irregular-date money weighting needs an explicit date-count convention. More complicated schedules with sign reversals can have multiple roots or no suitable root; a displayed solver output does not remove that interpretation problem.
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