The formula
saving = (balances + interest left) − (new principal + interest on the new loan)
Where it comes from
Refinancing means paying off what you owe with a new loan, and the honest comparison is not between interest rates but between totals: what you have left to pay if you carry on as you are against everything you will pay on the new loan, fees included. What you have already paid does not count, so each current debt is described by what is left of it. And there is a trap that shows up almost every time: the new loan stretches the term, the payment drops a lot and it feels like relief, but the total goes up because you are paying interest for more months.
How to work it out by hand
- For each current debt, work out the payment and the interest left from its balance, rate and months
- Add up the payments and the interest: that is where you stand today
- The new loan takes the sum of the balances plus the fees
- Work out its payment and interest with the new rate and term
- Compare the totals, not the payments
What is worth knowing
The figure that changes the decision is "new loan, but paying what you pay today": if you keep the payment you already make, the new loan clears before the current ones and there you really do save, because the rate is lower and you have stretched nothing. That is the refinancing that pays off. The one that does not is the one signed for the payment: it swaps three years of debt for five and ends up costing more, even though each month hurts less. The fees are financed on purpose, because that is what happens in practice: they are taken off the new loan or added to it, and either way you pay interest on them.