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Calculate required savings for school fees, accounting for inflation and investment returns.
This calculator determines how much you need to save each year to cover future school fees. It accounts for fee inflation, investment returns, and ensures you'll always have sufficient funds when payments are due, even with multiple children starting at different times.
The chart below shows how the required annual contribution changes across different combinations of fee inflation and investment return rates. The x-axis varies inflation around your input value, while each coloured line represents a different return rate. This helps you understand how sensitive your savings plan is to these uncertain assumptions: if returns are lower or inflation higher than expected, you'll need to save more.
The table provides a year-by-year breakdown showing your annual contribution, fee payments, investment returns, and running account balance. The row marked with an asterisk (*) is the binding constraint year, the point where your account balance is tightest (reaches zero). This is the year that determines your minimum required contribution.
The collapsible section at the bottom provides a rigorous derivation of the calculation methodology, including the balance evolution equations, geometric series simplifications, and the liquidity constraint that ensures your account never goes negative.
| Year | Contribution | Fee Payment | Investment Return | End Balance |
|---|
Money has time value: £1 today is worth more than £1 tomorrow because you can invest it and earn a return. This means we cannot directly add or compare amounts at different points in time; we must first move them to a common reference point.
Compounding (moving forward in time): If you invest £\(P\) today at annual return \(r\), after one year you have:
After \(t\) years, the balance grows to:
Discounting (moving backward in time): If you need £\(F\) in \(t\) years, the amount you must set aside today (the present value) is:
We have \(K\) children, where child \(k\) starts school in year \(Y_k\) (measured from today). Each child attends for \(n\) years. We also allow for a delay \(D \geq 0\) before saving begins, and an initial starting budget \(S \geq 0\). The core parameters are:
Timeline transformation: When \(D > 0\), we shift the timeline so that "Year 1" is when saving begins. This requires transforming the inputs:
All subsequent formulas use these transformed values \(A'\), \(Y'_k\), and \(S'\). For simplicity, we drop the primes and write \(A\), \(Y_k\), and \(S\) with the understanding that they represent the values at the time saving begins. We then define:
School fees grow with inflation from year 1. In calendar year \(t\), the fee for one child in school is:
Child \(k\) is in school during years \(Y_k, Y_k+1, \ldots, Y_k+n-1\). We define an indicator function:
The total fees in year \(t\) sum across all children in school that year:
where \(N_t = \sum_{k=1}^{K} \mathbf{1}_k(t)\) is the number of children in school during year \(t\).
Example: Two children with \(Y_1 = 2\) and \(Y_2 = 5\), each attending for \(n = 3\) years:
| Year \(t\) | Child 1 | Child 2 | \(N_t\) | Fee \(F_t\) |
|---|---|---|---|---|
| 1 | — | — | 0 | 0 |
| 2 | Year 1 | — | 1 | \(A(1+g)^1\) |
| 3 | Year 2 | — | 1 | \(A(1+g)^2\) |
| 4 | Year 3 | — | 1 | \(A(1+g)^3\) |
| 5 | — | Year 1 | 1 | \(A(1+g)^4\) |
| 6 | — | Year 2 | 1 | \(A(1+g)^5\) |
| 7 | — | Year 3 | 1 | \(A(1+g)^6\) |
Let \(I_t \in \{0, 1\}\) indicate whether we contribute in year \(t\), and let \(C\) be the annual contribution amount (what we solve for).
Mode 1 (save only before school starts):
Mode 2 (continue contributing during school):
Let \(B_t\) denote the account balance at the end of year \(t\). The timing within each year is:
This gives the recurrence relation:
We solve the recurrence by expanding it step by step. With starting budget \(S\):
The pattern becomes clear. At year \(t\):
We define the compounded starting budget:
This is the value at year \(t\) of the initial savings, growing at the investment return rate.
The accumulated contribution factor:
This is the future value at year \(t\) of £1 contributed in each contributing year.
And the accumulated fee value:
This is the future value at year \(t\) of all fees paid through year \(t\).
Substituting into our expanded recurrence gives the closed-form balance equation:
In practice, \(S_t\), \(A_t\), and \(V_t\) are computed iteratively using recurrence relations:
The fundamental requirement is that the account balance must never go negative:
Substituting the closed-form balance (6) into constraint (10):
The starting budget \(S_t\) effectively reduces the fee burden. Constraint (11) must hold for every year \(t\) where \(A_t > 0\). Therefore, the minimum contribution is:
The outer max ensures \(C_{\min} \geq 0\) (if the starting budget covers all fees, no contributions are needed). The year \(t^*\) where the inner maximum is achieved is the binding constraint year.
A naive present-value approach sets contributions equal to fees in present value terms, which is equivalent to enforcing only the terminal constraint \(B_T = 0\) from (10):
Comparing (13) with our solution (12), the naive approach fails when an intermediate year \(t < T\) has:
In this case, using \(C_{\text{naive}}\) in equation (6) gives \(B_t = S_t + C_{\text{naive}} \cdot A_t - V_t < 0\), so the account goes negative, requiring borrowing.
When does this happen? From equations (8) and (9), the ratio \((V_t - S_t) / A_t\) increases when fees are paid (adding to \(V_t\)) and decreases when contributions are made without corresponding fees (adding to \(A_t\)). An intermediate year becomes binding when:
Consider:
Fee schedule:
| Year | Children in school | Fee \(F_t\) |
|---|---|---|
| 1 | 0 | £0 |
| 2 | 3 (children 1,2,3) | £30,000 |
| 3 | 3 | £30,000 |
| 4 | 3 | £30,000 |
| 5 | 0 | £0 |
| 6 | 1 (child 4) | £10,000 |
| 7 | 1 | £10,000 |
| 8 | 1 | £10,000 |
Computing \(A_t\) and \(V_t\) using recurrences (8) and (9) with \(r = 0.05\) and \(S = 0\):
| Year \(t\) | \(A_t\) | \(V_t\) | \(V_t / A_t\) |
|---|---|---|---|
| 1 | 1.000 | 0 | 0 |
| 2 | 2.050 | 30,000 | 14,634 |
| 3 | 3.153 | 61,500 | 19,513 |
| 4 | 4.310 | 94,575 | 21,943 |
| 5 | 5.526 | 99,304 | 17,974 |
| 6 | 6.802 | 114,269 | 16,799 |
| 7 | 8.142 | 129,982 | 15,965 |
| 8 | 9.549 | 146,481 | 15,340 |
Applying equation (12) with \(S = 0\), the maximum ratio occurs at year 4 (value £21,943), not year 8. This is the binding constraint year \(t^* = 4\). Using the naive approach (13) would give \(C_{\text{naive}} = 15{,}340\), but substituting into (6) gives \(B_4 = 15{,}340 \times 4.310 - 94{,}575 = -28{,}470 < 0\), so the account goes negative.
The correct minimum contribution from (12) is \(C_{\min} = £21{,}943\) per year, ensuring \(B_t \geq 0\) for all \(t\) as required by (10).
The ratio \(\rho = \frac{1+g}{1+r}\) (appearing in the fee calculations) determines the relationship between fee growth and investment returns:
In Mode 1, once contributions stop (\(I_t = 0\)), examining equations (8) and (9) shows that \(A_t\) only grows by compounding while \(V_t\) grows by compounding plus new fees. Thus \((V_t - S_t) / A_t\) can only increase (when fees are paid) or stay constant (during gaps), so the binding constraint in (12) is always the terminal year. The naive approach (13) suffices.
In Mode 2, ongoing contributions (\(I_t = 1\)) add to \(A_t\) each year, which can cause the ratio \((V_t - S_t) / A_t\) to decrease during gap years or when fees drop. This is precisely when an intermediate year can become the binding constraint in (12), and the liquidity-aware calculation becomes essential.
Plan a Scottish property move: cash needed at completion, monthly costs, and sensitivity to assumptions. All rates per Revenue Scotland and Registers of Scotland.
This calculator models a Scottish property move: estimating the cash you need at completion, the ongoing monthly cost, and the sensitivity of those numbers to your inputs. It applies Scottish-specific rules — LBTT (not stamp duty), ADS (the additional-dwelling surcharge), Registers of Scotland dues, and the Home Report's role in capping mortgage lending.
Current Position covers your existing property, the costs of selling it, your cash savings, and your income. Estate agent fees in Scotland are typically 1–2% of sale price; sale solicitor fees usually £800–£1,500.
Target Purchase separates the Home Report value (what the surveyor says it's worth, which caps the mortgage) from the offer price (what you actually pay). LTV is your loan-to-value ratio against the Home Report. The bridging gap is the number of months between completing the purchase and completing the sale — if positive, ADS applies and is reclaimable later.
Other Upfront Costs are fees paid around completion: purchase solicitor, an optional buyer's survey beyond the Home Report, moving, first year's buildings insurance.
Monthly Running Costs are entered as annual £ amounts — the calculator divides by 12 for the headline figure.
Assumptions: investment return is used to compute the opportunity cost of ADS sitting with Revenue Scotland; property growth is used to project future equity in the amortisation table.
The four cards summarise: cash needed at completion (decomposed), funding available (savings plus net sale proceeds), the mortgage (loan amount, monthly payment, LTV, LTI), and the monthly total cost of ownership. The affordability stress test shows the monthly payment at your rate, plus 2 percentage points, plus 3 points — the kind of shock UK rates absorbed in 2022.
Three modes, switchable from the dropdown:
Year-by-year mortgage breakdown: interest, principal, remaining balance, and equity (assuming the chosen property-growth rate).
| Scenario | Rate | Mortgage £ | Total housing % of net |
|---|
| Year | Interest | Principal | Remaining | Property value | Equity |
|---|
LBTT is Scotland's transaction tax on residential property purchases, paid by the buyer. It is charged on a marginal banded basis: only the portion of the price falling within each band is taxed at that band's rate.
Current residential bands (unchanged for 2026–27):
| Band | Rate |
|---|---|
| £0 – £145,000 | 0% |
| £145,001 – £250,000 | 2% |
| £250,001 – £325,000 | 5% |
| £325,001 – £750,000 | 10% |
| Over £750,000 | 12% |
For a purchase price \(P\), with band lower thresholds \(l_i\), upper thresholds \(u_i\), and marginal rates \(r_i\):
Worked example — offer £475,000:
ADS is a flat 8% surcharge on the full purchase price, applied to any additional dwelling purchase of £40,000 or more. For someone moving home, ADS is triggered whenever the previous main residence has not yet been sold on the day of the new purchase. If the previous home is then sold within 36 months, the ADS is fully reclaimable from Revenue Scotland.
Although the ADS is fully refundable, it has a real economic cost: the 8% sits with Revenue Scotland for \(m\) months instead of earning your investment return \(r\). The opportunity cost (present value lost over the holding period) is:
This is the discount-factor formulation: the future £0.08·P refund is worth less than the £0.08·P paid today by exactly the factor \((1 - (1+r)^{-m/12})\). For \(m = 6\) months at \(r = 5\%\) on a £475,000 purchase: \(0.08 \times 475{,}000 \times (1 - 1.05^{-0.5}) \approx £917\). Small relative to the £38,000 gross outlay, but real cash.
In Scotland, mortgage lenders rely on the Home Report's surveyed valuation (or commission their own valuation, which typically aligns). They lend up to a chosen loan-to-value ratio against the lower of the Home Report value \(V\) and the offer price \(P\) — never the higher of the two.
where \(\ell\) is the loan-to-value ratio (e.g. 0.80 for 80% LTV). In the Scottish "Offers Over" market, \(P > V\) is common, and any premium above the Home Report value is entirely unsecured — you must pay it from cash:
Worked example — Home Report £450,000, offer £475,000, LTV 80%:
For a repayment mortgage of principal \(P\), monthly interest rate \(i = r/12\), and term of \(n\) months, each fixed monthly payment \(M\) covers the interest accrued on the outstanding balance plus a portion of principal. The balance after the \(k\)th payment satisfies the recurrence:
Expanding the recurrence and using the geometric series, the closed form is:
Applying the boundary condition \(B_n = 0\) (the mortgage is fully paid at term) and solving for \(M\):
For an interest-only mortgage, the monthly payment is simply \(M = P \cdot i\), and the full principal \(P\) is repaid as a balloon at term.
UK mortgage lenders are subject to the FCA's loan-to-income (LTI) flow limit: no more than 15% of a lender's new mortgages may be at LTI above 4.5×. In practice this means 4.5× gross household income is a soft cap for most borrowers.
Separately, lenders run affordability stress tests at rates above the offered product rate. This tool shows the monthly payment at the chosen rate, plus +2 and +3 percentage points, so you can see the impact of a rate shock similar to 2022's. As a rough check, total housing cost is often advised to stay below ~35% of net monthly income.
The affordability percentage compares total monthly housing costs to net monthly income, since housing bills come out of take-home pay (not gross). The tool assumes 100% of income is PAYE employment income for a Scottish taxpayer.
Scottish income tax 2026/27 (rates set by Holyrood; personal allowance and NI set at Westminster):
| Band | Income | Rate |
|---|---|---|
| Personal allowance | £0 to £12,570 | 0% |
| Starter | £12,571 to £16,537 | 19% |
| Basic | £16,538 to £29,526 | 20% |
| Intermediate | £29,527 to £43,662 | 21% |
| Higher | £43,663 to £75,000 | 42% |
| Advanced | £75,001 to £125,140 | 45% |
| Top | Over £125,140 | 48% |
The personal allowance is reduced by £1 for every £2 of gross income above £100,000, reaching zero at £125,140 (this taper is a UK rule, not a devolved one).
Class 1 employee National Insurance 2026/27 (UK-wide, not devolved):
| Range | Rate |
|---|---|
| Up to £12,570 (Primary Threshold) | 0% |
| £12,571 to £50,270 | 8% |
| Above £50,270 (Upper Earnings Limit) | 2% |
For gross annual income \(G\), the effective personal allowance is:
Income tax is the sum of band widths \(w_j\) at rates \(t_j\) applied to taxable income \(T = G - A(G)\):
where \(W_j = \sum_{k \le j} w_k\) is the cumulative band edge.
Employee NI follows the same band pattern, but on gross income (no allowance adjustment):
Net monthly take-home is then:
Worked example at gross £80,000:
Caveats. The model ignores pension contributions (which reduce taxable income), student loan repayments, salary sacrifice, the Marriage Allowance, Scottish dividend and savings tax treatment, and self-employed Class 2/4 NI. Treat the net figure as a sensible upper bound for take-home given your gross.
Registers of Scotland charges a banded registration fee when a transfer of ownership is recorded, based on the greater of consideration paid and property value:
| Value | Fee |
|---|---|
| Up to £50,000 | £80 |
| £50,001 – £100,000 | £140 |
| £100,001 – £150,000 | £260 |
| £150,001 – £200,000 | £400 |
| £200,001 – £300,000 | £530 |
| £300,001 – £500,000 | £660 |
| £500,001 – £700,000 | £800 |
| £700,001 – £1,000,000 | £930 |
| £1,000,001 – £2,000,000 | £1,100 |
| £2,000,001 – £3,000,000 | £3,300 |
| £3,000,001 – £5,000,000 | £5,500 |
| Over £5,000,000 | £8,250 |