One number: how to reduce a whole loan offer to a single rate
Suppose two banks make you an offer on the same property. One leads with 6.9%, the other with 7.4%. Which is cheaper? The honest answer is that the question cannot be answered from those two numbers, and it cannot be answered from any table of rates either. It can only be answered by pricing both sets of cash flows.
What the effective rate answers
The effective rate answers exactly one question, and it is the right one:
If this loan had a single fixed interest rate for its whole term, and no fees of any kind, what would that rate have to be for me to pay precisely what I am actually paying?
Everything collapses into that number. A generous promotion followed by a fat margin, a modest promotion followed by a thin one, an arrangement fee, insurance sold at drawdown, an early settlement penalty: all of it is just cash leaving your account on particular dates, and the effective rate is the one rate consistent with that pattern of dates and amounts.
How it is computed
It is an internal rate of return, solved rather than calculated. There is no closed-form formula, so you search for the rate that makes the whole series balance.
- Month zero is what you actually receive. Not the amount borrowed: the amount borrowed less anything deducted at drawdown. On a 2.4 billion dong loan with 15,000,000 dong of arrangement, valuation, notary and security registration fees, you receive 2,385,000,000 dong. If insurance of 6% is taken upfront, you receive 2,241,000,000 dong.
- Every month after that is what leaves your account. Interest plus principal plus any fee charged that month.
- A settlement adds a final lump. The outstanding balance, the early repayment fee and the clawback, all in the settlement month.
- Solve. Find the monthly rate at which the present value of everything in step two and three exactly equals the amount in step one. The loan inspector does it by two hundred rounds of bisection, then annualises by compounding, so 1% a month becomes 12.6825% a year rather than 12%.
The compounding step matters and is often skipped. A rate of 1% a month is not 12% a year, because the twelfth month’s interest is charged on a base that has already borne eleven months of interest. Comparing a monthly figure multiplied by twelve against a properly annualised figure understates the first by about two thirds of a point at these levels.
The same loan, six ways
Below is the loan used throughout this site, 2.4 billion dong over twenty years, promotional 6.9% for twelve months then 8.5% base plus a 3 point margin, with one variable changed at a time. The headline rate is 6.9% in every row.
| Variant | Total cost above principal | Effective rate |
|---|---|---|
| Equal principal, held to term | 2,678,630,000 | 11.392% |
| Equal instalments, held to term | 3,610,585,609 | 11.509% |
| Flat interest on the original principal | 5,424,600,000 | 16.233% |
| Equal principal plus 6% insurance at drawdown | 2,822,630,000 | 12.642% |
| Equal principal, floating rate two points higher | 3,113,730,000 | 13.168% |
| Equal principal, settled in month 24 | 583,750,000 | 13.014% |
Six loans, one headline rate, effective rates from 11.392% to 16.233%. Nothing in the advertising distinguishes them.
Two things the table shows that are easy to miss
Total cost and effective rate do not rank the same way
Equal instalments cost 931,955,609 dong more than equal principal in absolute terms, but the effective rate differs by only 0.117 of a percentage point. That is not a contradiction. Equal instalments leave more capital outstanding for longer, so you are borrowing more money for more months; the price per dong per year is almost the same, you are simply buying more of it. Which measure matters depends on the question. If you are asking “is this bank charging me a fair price”, use the effective rate. If you are asking “how much of my life does this cost”, use total cost.
An upfront fee hits the rate far harder than its size suggests
Insurance at 6% of the loan is 144,000,000 dong, about 5% of the total cost of the loan. But it moves the effective rate by 1.25 percentage points, from 11.392% to 12.642%, because it is paid on day one and therefore weighs on every one of the 240 months that follow. Money leaving early is expensive in a way that money leaving late is not. This is the whole reason upfront charges deserve separate scrutiny, covered in loan insurance sold with the mortgage.
Using it to choose between two banks
Collect the same eight inputs from each offer, then run both. Nothing else is required.
- Amount borrowed and term in months.
- Promotional rate and how many months it runs.
- Base rate today, and the margin.
- Everything payable at drawdown, including insurance if it is a condition.
- The early repayment tiers and the clawback window, if you might move.
Then compare on two numbers rather than one: the effective rate, and the instalment in the month after the promotion ends. The first tells you which loan is cheaper. The second tells you whether you can survive it, which is a different question and is answered in how much can you actually borrow.
What it deliberately does not include
The effective rate here prices the credit agreement and nothing else. It excludes property taxes, building management fees, maintenance, insurance you would have bought anyway, and any movement in the value of the property. It also assumes the floating rate you enter holds for the rest of the term, which it will not; that is why the tool offers a stress test rather than a forecast. A single number is only useful if you know precisely what it is a number for.