Rate shopping gets most of the attention in conversations about debt, and it is worth doing.
But for many people the rate is the smaller of the two levers available, and the larger one —
the size of the balance and how fast it falls — receives far less thought.
Interest is charged on a quantity
A rate is a multiplier; it only produces a cost when applied to a balance. Reducing the rate
by a few points lowers the cost of whatever you owe. Reducing the balance lowers the cost and
shortens the period over which any cost is charged at all. The second effect is cumulative,
which is why extra principal payments do disproportionate work.
This is also why a lower rate obtained alongside a longer term can leave someone worse off.
The multiplier improved and the quantity it applies to persisted for longer.
Where to put the effort
In practice both are worth pursuing, in a specific order. Ask for a lower rate first, because
it costs one phone call and takes ten minutes; existing customers in good standing are told yes
more often than most people expect. Then direct every available amount at the principal of the
most expensive balance and keep the payment fixed as the balance falls.
Fixing the payment is the part that gets skipped. Minimum payments decline as the balance
declines, which quietly extends the timeline. Holding the payment at its original level turns the
entire reduction into acceleration.
