Loans & Mortgages
How To Compare Loan Offers
Two loan offers can be compared on the monthly payment or on the total cost. The two rankings are often different, and the difference is exactly what the fee is for.
Quick Answer
payment = principal x r / (1 - (1+r)^-n); total cost = payment x n - principal + upfront fee
- P
- Principal borrowed, the same for both offers
- r
- Monthly interest rate, the annual rate divided by twelve
- n
- Number of monthly payments
- C
- Total cost of credit, interest plus any upfront fee
£25,000 over five years at 5.5% with a £250 fee costs £3,901.74 in total. Over seven years at 4.9% with no fee the total is £4,582.63, even though the monthly payment is £125.35 lower.
What Is How To Compare Loan Offers?
Comparing loan offers means putting two amortisation schedules side by side. Both the monthly payment and the total cost of credit have to be computed for each, because the ranking on one does not have to match the ranking on the other.
The monthly payment is what the borrower feels. It is fixed for the life of the loan and it determines whether the repayment is affordable, so it is the number most people compare first.
The total cost of credit is what the borrowing actually costs. It is all the interest paid over the term plus any fee charged upfront, and it ignores how painful each individual payment is.
A longer term lowers the monthly payment and raises the total cost, because the principal is outstanding for longer. That trade is the single most common source of a wrong comparison.
A lower rate is not always the cheaper loan. A 4.9% loan over seven years costs more in total than a 5.5% loan over five years, because the extra two years of interest outweigh the smaller rate.
An upfront fee has to be added to the interest, not compared with it. A £250 fee paid on day one is worth less than £250 of interest paid over five years, because the interest is paid later.
The honest comparison is total cost of credit, which adds the fee to the interest without discounting. This slightly overstates the fee's cost, which is the conservative direction for a comparison.
The monthly payment is the discounted figure, in the sense that a longer term spreads the same principal further. It is the right measure for affordability and the wrong measure for cost.
Affordability matters when the payment is the binding constraint. If the lower monthly payment is the only way the loan is manageable, the higher total cost is the price of that flexibility.
Adding a fee to a lower rate changes the ranking only when the fee is large relative to the interest saving. On a long loan with a small balance, a £250 fee can be worth more than a whole percentage point of rate.
The annual percentage rate is designed to roll both effects into one number. It converts the upfront fee into an equivalent rate, so comparing APRs is legitimate when both loans have the same term.
When the terms differ, the APR comparison is misleading. A long loan has a low APR because the fee is spread over many payments, and yet it can still cost far more in total.
Comparing on the total cost of credit is the cleaner rule when the terms differ, because it is a single cash figure that already accounts for both the rate and the length.
The calculator prices both offers, shows the monthly payment for each and the total cost of credit for each, adds the upfront fee to the interest, and reports the difference between the two.
Formula
M = P x r / (1 - (1+r)^-n)
The payment that clears the principal exactly over n payments, with interest charged monthly on the outstanding balance. Negative exponents are allowed directly in the expression.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| P | Principal | currency | The amount borrowed. |
| r | Monthly rate | percent | Annual rate divided by twelve. |
| n | Payments | months | Months in the term. |
| M | Monthly payment | currency | The fixed payment each month. |
C = (M x n - P) + upfront fee
Everything paid goes to the principal or the interest, so subtracting the principal from the total paid isolates the interest. Adding the upfront fee gives the whole cost of the borrowing.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| M | Monthly payment | currency | The fixed payment each month. |
| n | Payments | months | Months in the term. |
| P | Principal | currency | The amount borrowed. |
| F | Upfront fee | currency | Any charge paid at the start. |
| C | Total cost | currency | Interest plus fee. |
How To Calculate How To Compare Loan Offers
- 1
Convert each annual rate to a monthly one
Divide each offer's rate by twelve. A 5.5% offer has a monthly rate of 0.4583%, and every figure below is driven by that monthly figure.
- 2
Compute the monthly payment for each offer
Use the amortisation formula with the number of months in each term. The same principal at a longer term always produces a smaller monthly payment.
- 3
Multiply out to find the interest
Payment times months gives everything paid. Subtracting the original principal leaves the interest, which grows with the term far faster than the rate changes.
- 4
Add any upfront fee to the interest
The fee is a cash cost of the borrowing, so it is added to the interest. This is conservative, because it does not discount the fee for being paid early.
- 5
Compare the two totals, and the two payments separately
Rank on total cost for the cheap answer and on monthly payment for the affordable answer. When the two rankings disagree, the term length is the reason.
Examples
Example 1: A short loan at a higher rate against a long loan at a lower rate
- Principal
- £25,000
- Offer A rate
- 5.5%
- Offer A term
- 5
- Offer A fee
- £250
- Offer B rate
- 4.9%
- Offer B term
- 7
- Offer B fee
- £0
| Step | Calculation | Result |
|---|---|---|
| Offer A monthly payment | £25,000 x 0.004583 / (1 - 1.004583^-60) | 477.53 |
| Offer A total paid | £477.53 x 60 | 28651.74 |
| Offer A interest | £28,651.74 - £25,000 | 3651.74 |
| Offer A total cost | £3,651.74 + £250 | 3901.74 |
| Offer B monthly payment | £25,000 x 0.004083 / (1 - 1.004083^-84) | 352.17 |
| Offer B total cost | £352.17 x 84 - £25,000 | 4582.63 |
| Monthly payment saving on offer B | £477.53 - £352.17 | 125.35 |
Result: Offer A costs £477.53 a month and £3,901.74 in total. Offer B costs £352.17 a month, £125.35 less, but £4,582.63 in total, so the two extra years cost £680.89 more than the lower rate saves. Offer A is cheaper, offer B is easier to afford.
Example 2: A fee that outweighs a lower rate
- Principal
- £8,000
- Offer A rate
- 7.0%
- Offer A term
- 3
- Offer A fee
- £0
- Offer B rate
- 6.5%
- Offer B term
- 3
- Offer B fee
- £220
| Step | Calculation | Result |
|---|---|---|
| Offer A monthly payment | £8,000 x 0.005833 / (1 - 1.005833^-36) | 247.02 |
| Offer A total cost | £247.02 x 36 - £8,000 | 892.60 |
| Offer B monthly payment | £8,000 x 0.005417 / (1 - 1.005417^-36) | 245.19 |
| Offer B interest | £245.19 x 36 - £8,000 | 826.91 |
| Offer B total cost | £826.91 + £220 | 1046.91 |
| Offer A advantage | £1,046.91 - £892.60 | 154.31 |
Result: Both offers run for three years, so the lower rate should win. Offer B's monthly payment is £1.82 lower, but its £220 fee takes the total cost to £1,046.91 against £892.60 for offer A, so offer A is £154.31 cheaper overall.
Calculator
Cheaper offer saves
$680.89
- Monthly payment difference
- $125.35
- Offer A monthly payment
- $477.53
- Offer B monthly payment
- $352.17
- Offer A total cost of credit
- $3,901.74
- Offer B total cost of credit
- $4,582.63
- Offer A interest
- $3,651.74
- Offer B interest
- $4,582.63
Values update as you type. This calculator covers the single scenario its formula assumes — see Common Mistakes for what it leaves out.
Prefer a full-width tool? Open the How To Compare Loan Offers calculator page.
Common Mistakes
Comparing only the monthly payment
A longer term always gives a smaller payment and always costs more in total. Ranking on the payment alone systematically favours the longest loan on the list.
Comparing only the interest rate
The rate ignores the term and the fee. A 4.9% loan over seven years can cost far more than a 5.5% loan over five, and a big fee can outweigh a whole point of rate.
Treating an upfront fee as equivalent to the same amount of interest
Interest is paid over years while the fee is paid at the start. Adding them without discounting is conservative, but comparing the fee to a single year's interest is not a comparison at all.
Using the APR when the terms differ
The APR spreads the fee over the number of payments, so a long loan gets a flattering APR. When the terms differ, compare total cost of credit instead.
Forgetting that the principal is the same in both offers
The comparison only works if both offers fund the same amount. Borrowing a little more to cover a fee changes the total and invalidates the ranking.
Ignoring the term the borrower actually wants
If the loan is for a purchase that will be replaced in three years, a seven-year term is not a cheaper option but a different decision, because the asset outlives the debt only in the wrong direction.
Assuming a longer term can be fixed later
Overpaying shortens a loan only if the terms allow it without penalty. Many agreements restrict overpayments, which removes the flexibility the comparison assumed.
FAQ
How do I compare two loan offers properly?
Compute the monthly payment and the total cost of credit for each. Rank on total cost to find the cheap answer and on monthly payment to find the affordable one, and expect the two rankings to disagree when the terms differ.
Why is a longer loan cheaper per month but more expensive overall?
The principal is outstanding for longer, so more interest accrues on it. Spreading the same amount over more payments lowers each payment while raising the sum of all of them.
Should I compare the monthly payment or the total cost?
Both, for different reasons. The total cost answers which loan is cheaper, and the monthly payment answers whether you can service it. If only one is affordable, that constraint decides.
How do upfront fees change the comparison?
They are added to the interest to give the total cost of credit. On a short loan with a small balance a fee can outweigh a full percentage point of rate, which is why the fee has to be in the total.
Is comparing APRs enough?
Only when both loans have the same term. The APR spreads the fee over the payments, so it flatters longer terms. With different terms, total cost of credit is the cleaner measure.
Can a longer loan ever be the right choice?
Yes, when the lower payment is the only affordable one and the extra interest is the price of that flexibility. It is a deliberate trade rather than a free improvement.
References
- [1]Consumer Financial Protection Bureau, Comparing loan offers — https://www.consumerfinance.gov/ask-cfpb/how-can-i-compare-loans-from-different-lenders-en-1441/
- [2]Consumer Financial Protection Bureau, Loan Estimate form and instructions — https://www.consumerfinance.gov/rules-policy/regulations/1024/37/
- [3]Consumer Financial Protection Bureau, Annual percentage rate explained — https://www.consumerfinance.gov/ask-cfpb/what-is-the-difference-between-an-interest-rate-and-the-annual-percentage-rate-en-37/