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Worked example library

Worked Mortgage Examples

Browse realistic UK mortgage scenarios for affordability, repayments, comparisons, overpayments, remortgaging, and offset mortgages. Each example shows the assumptions, the calculation, the final estimate, and the calculator to test your own numbers.

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All worked examples

6 examples showing the full calculation.

Affordability

First-time buyer affordability check

Scenario

Priya and Sam earn a combined £72,000 before tax and have saved a £45,000 deposit. They want to know the upper edge of a sensible search budget before speaking to a broker.

Try the affordability calculator

Assumptions

  • Illustrative lender income multiple: 4.5x combined gross income.
  • Monthly comfort check uses an estimated £1,800 maximum mortgage payment.
  • Repayment estimate uses a 25-year term at 4.8% interest.
  • This is not a lender decision or mortgage advice.

Worked example

Full calculation

Estimated purchase budget
\[\begin{aligned}B_{estimate} &= I_{gross} \times k \\ V_{budget} &= B_{estimate} + D \\ \operatorname{LTV} &= \frac{B_{estimate}}{V_{budget}} \times 100\end{aligned}\]
\(B_{estimate}\)
borrowing estimate
\(I_{gross}\)
combined gross annual income
\(k\)
income multiple
\(V_{budget}\)
estimated property budget
\(D\)
deposit
\(\operatorname{LTV}\)
loan-to-value percentage

  1. Estimate borrowing from income

    Multiply combined gross income by the illustrative income multiple.

    \[£72{,}000 \times 4.5 = £324{,}000\]

  2. Add the deposit to estimate a property budget

    The purchase budget combines the mortgage estimate with the deposit cash.

    \[£324{,}000 + £45{,}000 = £369{,}000\]

  3. Check loan-to-value

    LTV helps show how much of the property price would be funded by the mortgage.

    \[£324{,}000 / £369{,}000 \times 100 = 87.8\%\]

  4. Sense-check the estimated payment

    A £324,000 mortgage over 25 years at 4.8% gives an estimated payment of about £1,857, which is above the £1,800 comfort check.

Income-based borrowing estimate
£324,000
Estimated property budget
£369,000
Estimated LTV
87.8%
Estimated monthly payment
About £1,857
Based on 25 years at 4.8%, before fees and lender checks.

Final result

The income multiple points to a £369,000 purchase budget, but the payment check suggests Priya and Sam may want to test a slightly lower price or a larger deposit.

Mortgage Repayment

Repayment estimate for a UK home purchase

Scenario

A buyer is looking at a £310,000 home with a £62,000 deposit and wants a quick monthly repayment estimate before comparing mortgage products.

Try the mortgage repayment calculator

Assumptions

  • Repayment mortgage.
  • Mortgage term: 25 years.
  • Illustrative interest rate: 4.6%.
  • Fees, insurance, and future rate changes are excluded.

Worked example

Full calculation

Repayment mortgage formula
\[M = \frac{P r}{1 - (1 + r)^{-n}}\]
\(M\)
estimated monthly repayment
\(P\)
mortgage balance or principal
\(r\)
monthly interest rate as a decimal
\(n\)
number of monthly payments

P is mortgage balance, r is monthly interest rate, n is the number of monthly payments, and M is the estimated monthly payment.

  1. Find the mortgage balance

    Subtract the deposit from the property price.

    \[£310{,}000 - £62{,}000 = £248{,}000\]

  2. Convert rate and term

    Convert the annual interest rate into a monthly decimal, and the term into months.

    \[\begin{aligned}r = 4.6\% / 12 / 100 = 0.003833 \\ n = 25 \times 12 = 300\end{aligned}\]

  3. Estimate the monthly repayment

    Put the balance, monthly rate, and number of payments into the repayment formula.

    \[M = 248{,}000 \times 0.003833 / (1 - (1 + 0.003833)^-300) = £1{,}390.28\]

  4. Estimate total repaid and interest

    Multiply the monthly estimate by 300 payments, then subtract the original mortgage balance.

    \[\begin{aligned}\text{Total repaid} = £1{,}390.28 \times 300 = £417{,}084 \\ \text{Interest} = £417{,}084 - £248{,}000 = £169{,}084\end{aligned}\]
Mortgage balance
£248,000
Monthly repayment
About £1,390
Total repaid
About £417,084
Total interest
About £169,084

Final result

At 4.6% over 25 years, the buyer would estimate a monthly repayment of about £1,390 and total interest of about £169,084 if the rate stayed the same.

Mortgage Comparison

Comparing two fixed-rate mortgage deals

Scenario

A homeowner needs a £220,000 repayment mortgage over 25 years and is comparing two 5-year fixed deals: one with a lower rate and fee, and one with no product fee.

Try the mortgage comparison tool

Assumptions

  • Deal A: 4.29% with a £999 product fee.
  • Deal B: 4.49% with no product fee.
  • Comparison period: first 60 months of the mortgage.
  • Both examples exclude valuation, legal, and broker fees.

Worked example

Full calculation

Five-year modelled cost
\[\begin{aligned}C_{fix} &= \sum_{m=1}^{60} P_m + F_{product} \\ B_{60} &= \text{remaining balance after 60 months}\end{aligned}\]
\(C_{fix}\)
cost during the fixed period
\(P_m\)
payment in month m
\(F_{product}\)
product fee
\(B_{60}\)
remaining balance after 60 months

  1. Calculate each monthly payment

    Use the repayment formula with a £220,000 balance, 25-year term, and each fixed rate.

    Deal A monthly payment
    About £1,196
    Deal B monthly payment
    About £1,223

  2. Compare five years of payments

    Multiply each monthly payment by 60 months, then add any product fee.

    \[\begin{aligned}\text{Deal A} = £1{,}196 \times 60 + £999 = £72{,}759 \\ \text{Deal B} = £1{,}223 \times 60 + £0 = £73{,}380\end{aligned}\]

  3. Check the remaining balance

    A lower rate can also leave a slightly lower balance at the end of the fix.

    Deal A balance after 5 years
    About £193,788
    Deal B balance after 5 years
    About £194,452
Deal A five-year payment cost
About £72,759
Includes the £999 product fee.
Deal B five-year payment cost
About £73,380
Payment-cost difference
About £621
Balance difference after 5 years
About £664
Deal A leaves the lower estimated balance.

Final result

Deal A is estimated to cost about £621 less in payments and fees over five years, and may also leave the balance about £664 lower.

Overpayments

Monthly overpayment interest saving

Scenario

A homeowner owes £180,000, has 23 years remaining, and is considering a regular £200 monthly overpayment while the rate is 4.5%.

Try the overpayment calculator

Assumptions

  • Repayment mortgage with 23 years remaining.
  • Current rate held constant at 4.5% for the estimate.
  • Regular overpayment: £200 per month.
  • Early repayment charge limits are not modelled in this example.

Worked example

Full calculation

Monthly balance update
\[\begin{aligned}I_m &= B_t \times \frac{R}{12 \times 100} \\ B_{t+1} &= B_t + I_m - P_m - O_m\end{aligned}\]
\(I_m\)
estimated monthly interest
\(B_t\)
balance before this month's payment
\(R\)
annual interest rate as a percentage
\(B_{t+1}\)
balance after this month's payment
\(P_m\)
standard monthly repayment
\(O_m\)
monthly overpayment

  1. Estimate the standard payment

    For £180,000 over 23 years at 4.5%, the standard repayment is about £1,053 per month.

  2. Compare the monthly cash going to the mortgage

    Adding £200 raises the monthly mortgage payment from about £1,053 to about £1,253.

    \[£1{,}053 + £200 = £1{,}253\]

  3. Estimate the payoff impact

    Running the monthly balance update until the balance reaches zero gives a shorter payoff period.

    Without overpayment
    276 months
    23 years.
    With £200 overpayment
    About 218 months
    About 18 years and 2 months.

  4. Estimate interest saved

    Total interest is the sum of monthly interest charged across the mortgage. The overpayment reduces the balance faster, so future interest is lower.

Standard monthly repayment
About £1,053
Overpayment plan payment
About £1,253
Estimated time saved
About 4 years 10 months
Estimated interest saved
About £27,900

Final result

A £200 monthly overpayment could reduce the estimated mortgage term by nearly five years and save around £27,900 interest, assuming the rate and payments stayed unchanged.

Remortgaging

Remortgage break-even after fees

Scenario

A homeowner owes £185,000 with 20 years left. Their current rate is 5.7%, and a new deal at 4.65% has a £999 product fee plus £300 legal and valuation costs.

Try the remortgage comparison calculator

Assumptions

  • Current and new payments are estimated over the same remaining 20-year term.
  • Switching costs total £1,299.
  • No early repayment charge is included.
  • Comparison period: 24 months.

Worked example

Full calculation

Break-even estimate
\[\begin{aligned}S_m &= P_{current} - P_{new} \\ m_{\text{break even}} &= \frac{C_{switch}}{S_m} \\ S_{2yr} &= S_m \times 24 - C_{switch}\end{aligned}\]
\(S_m\)
estimated monthly saving
\(P_{current}\)
current monthly payment
\(P_{new}\)
new monthly payment
\(m_{\text{break even}}\)
months to break even
\(C_{switch}\)
switching costs
\(S_{2yr}\)
two-year net saving

  1. Estimate the current payment

    A £185,000 repayment mortgage over 20 years at 5.7% is about £1,294 per month.

  2. Estimate the new payment

    The same balance and term at 4.65% is about £1,186 per month.

  3. Find the monthly saving

    Subtract the new estimated payment from the current estimated payment.

    \[£1{,}294 - £1{,}186 = \text{£108 per month}\]

  4. Calculate break-even and two-year saving

    Divide switching costs by the monthly saving, then compare the saving over 24 months.

    \[\begin{aligned}\text{Break} - \text{even} = £1{,}299 / £108 = \text{12.0 months} \\ \text{Two} - \text{year net saving} = £108 \times 24 - £1{,}299 = £1{,}293\end{aligned}\]
Current estimated payment
About £1,294
New estimated payment
About £1,186
Break-even point
About 12 months
Estimated two-year net saving
About £1,293

Final result

The lower rate could repay the £1,299 switching costs after about 12 months and leave an estimated £1,293 net saving after two years.

Offset Mortgages

Offset savings interest reduction

Scenario

A homeowner has a £240,000 offset mortgage at 5.1% and keeps £35,000 in linked savings. They want to estimate the first month of interest reduction.

Try the offset mortgage calculator

Assumptions

  • Linked savings reduce the balance charged interest.
  • The savings stay accessible but do not earn separate savings interest in this example.
  • Monthly interest is simplified as annual rate divided by 12.
  • Tax, fees, and changing daily balances are excluded.

Worked example

Full calculation

Offset interest calculation
\[\begin{aligned}B_{interest} &= B_{mortgage} - S_{offset} \\ I_m &= B_{interest} \times \frac{R}{12 \times 100}\end{aligned}\]
\(B_{interest}\)
balance charged interest
\(B_{mortgage}\)
mortgage balance
\(S_{offset}\)
linked offset savings
\(I_m\)
estimated monthly interest
\(R\)
annual interest rate as a percentage

  1. Find the balance charged interest

    Subtract the linked savings from the mortgage balance. The mortgage balance is still £240,000, but interest is charged on the smaller amount.

    \[£240{,}000 - £35{,}000 = £205{,}000\]

  2. Calculate monthly interest without offset savings

    This is the rough first-month interest if the full balance were charged interest.

    \[£240{,}000 \times 5.1\% / 12 = £1{,}020\]

  3. Calculate monthly interest with offset savings

    Apply the same rate to the reduced interest balance.

    \[£205{,}000 \times 5.1\% / 12 = £871.25\]

  4. Estimate the monthly interest reduction

    Subtract offset interest from the standard interest estimate.

    \[£1{,}020 - £871.25 = £148.75\]
Mortgage balance
£240,000
Interest-charged balance
£205,000
First-month interest reduction
About £149
Simple annualised reduction
About £1,785
£148.75 x 12 before balance changes.

Final result

Keeping £35,000 in linked savings could reduce the first month's mortgage interest by about £149, while preserving access to the cash.