One rate for several balances
Two loans at different rates do not average to the midpoint. The rate you are really paying is weighted by how much sits at each — and that weighted figure, the blended rate, is what you compare a consolidation or refinance offer against. This calculator computes it from two balances and two rates.
The formula
Worked example: $10,000 at 5% and $5,000 at 8%
- Annual interest: 500 + 400 = $900
- Total balance: $15,000
- Blended rate: 900 / 15,000 = 6.0%
The simple average of 5% and 8% is 6.5%. The blended rate is lower because two thirds of the money is at the cheaper rate. The half-point gap is $75 a year on this balance and would mislead any comparison.
Where the weighting takes the rate
| Balance at 5% | Balance at 8% | Blended |
|---|---|---|
| $10,000 | $5,000 | 6.00% |
| $5,000 | $10,000 | 7.00% |
| $7,500 | $7,500 | 6.50% |
| $14,000 | $1,000 | 5.20% |
Swap the balances and the blended rate moves a full point on the same two loans. Only with equal balances does it equal the simple average.
Reading a consolidation offer
A single loan at 6.5% for the full $15,000 looks like it sits between the two existing rates and might seem neutral. It is a half-point increase on the blended 6.0% — $75 a year more, and over a five-year term about $200 in extra interest before fees. Any consolidation offer above the blended rate costs money; the convenience of one payment is what you are buying.
The reverse also holds. Paying extra on the 8% loan first, rather than splitting the overpayment, lowers the blended rate fastest — the logic behind the avalanche method.
Mortgages and the same arithmetic
A first mortgage at 3% and a home-equity line at 8% blend to a single rate the same way. Homeowners deciding whether to refinance everything into one new loan at 6% are comparing 6% against that blend, and with a large low-rate first mortgage the blend is often well under 4% — refinancing would raise the rate on the whole balance.
What this calculator leaves out
Different remaining terms, which change how long each rate applies; fees on a consolidation; and the fact that the blend drifts as the balances amortise at different speeds.
Related calculators
- Weighted average cost of capital — the same weighting across equity and debt
- Debt consolidation calculator — the offer against the blend, with fees
- Debt avalanche — which balance to attack first