How the Engine Works
Isaac's projection engine runs a year-by-year simulation from your current age to age 100. Each year, it moves through one of three phases:
The engine accounts for fractional years — if your birthday is in July, only the remaining months of your first year are compounded, giving month-accurate projections from day one.
Pension Growth (Accumulation)
During accumulation, your Defined Contribution (DC) pension pot grows through monthly compounding. Each month, your contributions are added and investment returns are applied.
For each month:
pot = (pot + monthlyContribution) × (1 + monthlyReturn)
This is repeated 12 times per year (or fewer in the first and last years, for accuracy). Your contribution can be a fixed amount or linked to inflation, and an optional contribution growth rate can increase your payments each year during accumulation.
ISA & Savings
ISAs, other investments, and cash savings are tracked separately from your DC pension pot. Each follows the same monthly compounding formula but with its own rate of return, keeping tax-free ISA growth distinct from pension growth.
State Pension
The new State Pension is calculated based on your National Insurance qualifying years. You need a minimum of 10 qualifying years to receive anything, and 35 years for the full amount.
The current full new State Pension is £241.30 per week (2026/27 rate). It's payable from your State Pension age and is treated as taxable income in the projection.
If you choose to defer your State Pension, Isaac delays when payments begin but does not currently model deferral uplifts.
Defined Benefit Pensions
Defined Benefit (DB) pensions pay a guaranteed annual income from your scheme's normal retirement age. Isaac models the revaluation (growth) of your DB pension up to retirement, subject to an inflation cap set by your scheme.
currentValue = basePension × (1 + cappedGrowth)years
Once in payment, the DB pension is added to your gross income each year and taxed accordingly. You can add multiple DB pensions, each with its own start age and inflation rules.
Income Tax
Isaac calculates income tax using the current HMRC rates for either England/Wales or Scotland. All taxable income sources (DC withdrawals, DB pensions, State Pension, extra income) are combined, and tax is calculated on the total.
Personal Allowance Taper
If your total income exceeds £100,000, your Personal Allowance is reduced by £1 for every £2 above the threshold, until it reaches zero.
England & Wales Bands (2026/27)
| Band | Taxable Income | Rate |
|---|---|---|
| Personal Allowance | Up to £12,570 | 0% |
| Basic rate | £12,571 - £50,270 | 20% |
| Higher rate | £50,271 - £125,140 | 40% |
| Additional rate | Over £125,140 | 45% |
Scottish Bands (2026/27)
| Band | Taxable Income | Rate |
|---|---|---|
| Personal Allowance | Up to £12,570 | 0% |
| Starter rate | £12,571 - £16,538 | 19% |
| Basic rate | £16,539 - £29,527 | 20% |
| Intermediate rate | £29,528 - £62,430 | 21% |
| Higher rate | £62,431 - £125,140 | 42% |
| Advanced rate | £125,141 - £150,000 | 45% |
| Top rate | Over £150,000 | 48% |
Tax Band Growth
By default, tax bands are frozen (as per current HMRC policy until 2028). You can optionally model tax band growth, which increases thresholds by inflation each year — useful for longer projections where bands may eventually be uprated.
Tax-Free Lump Sum
When you retire, you can take some of your DC pension pot as a tax-free lump sum. Isaac supports three methods:
Upfront (Pension Commencement Lump Sum)
A percentage of your pot is taken as a tax-free lump sum at retirement, up to a maximum of 25% and subject to the £268,275 Lump Sum Allowance.
Gradual (UFPLS)
With Uncrystallised Funds Pension Lump Sum, 25% of each withdrawal is tax-free and 75% is taxed as income. The tax-free portion is tracked against the £268,275 lifetime limit. Each person (including your partner) has their own independent cap.
Hybrid
Take a fixed £ amount upfront at retirement, then use UFPLS for subsequent withdrawals. The remaining Lump Sum Allowance carries forward.
Drawdown & Withdrawals
In retirement, Isaac calculates how much to withdraw from your pension pot each year to meet your spending target, after accounting for guaranteed income (State Pension, DB pensions, extra income).
Tax-Efficient Withdrawal Ordering
The engine uses an optimised withdrawal sequence:
- First, guaranteed income fills the Personal Allowance (tax-free)
- Then, DC withdrawals are taken to fill the remaining basic rate band
- ISA and savings (tax-free) are drawn to avoid higher-rate tax
- Finally, additional DC withdrawals cover any remaining shortfall
Gross-Up Calculation
When you need a specific net income, Isaac uses binary search to find the gross withdrawal that produces the right amount after tax. This ensures you withdraw only what's needed, minimising unnecessary tax.
Drawdown Strategies
- Flexible drawdown — withdraw what you need each year from your DC pot
- Annuity purchase — buy a guaranteed income at a specified age, funded from one or more DC pots
- Blended — combine flexible drawdown with a partial annuity purchase
An optional emergency fund can be set aside, excluded from drawdown calculations.
Earliest Retirement Age
Isaac can calculate the earliest age at which you can retire and still have your money last to a target age (default: 90).
For each candidate age, it runs a full projection.
If the pot lasts → try an earlier age.
If the pot runs out → try a later age.
The search converges to the earliest viable retirement age.
This accounts for all income sources, tax, spending, and inflation — it's a full projection at each step, not a simplified estimate.
Inflation & Growth
Inflation affects spending targets, pension values, and tax bands throughout the projection.
- Default inflation rate: 2.5% per year (adjustable)
- Spending: your target spending increases with inflation each year
- State Pension: uprated by inflation annually (triple lock approximation)
- DB pensions: revalued by inflation, subject to scheme caps
- Tax bands: frozen by default, optionally grow with inflation
Investment Scenarios
You can model three investment scenarios — optimistic, base, and pessimistic — to see how different market conditions affect your retirement. Each uses a different annual return rate applied to the same compounding formula.
Post-Retirement Returns
The default post-retirement investment return is 3.5%, reflecting a more conservative portfolio. This is applied to your remaining pot during drawdown, separately from the accumulation-phase return.
Current Rates & Thresholds (2026/27)
| Parameter | Value |
|---|---|
| Personal Allowance | £12,570 |
| Basic rate upper limit (England/Wales) | £50,270 |
| Higher rate upper limit | £125,140 |
| PA taper threshold | £100,000 |
| Lump Sum Allowance | £268,275 |
| State Pension (full, new) | £241.30/week |
| State Pension age | 67 (rising to 68) |
| Min. NI qualifying years | 10 |
| Full NI qualifying years | 35 |
| Money Purchase Annual Allowance | £10,000 |
| Default inflation | 2.5% |
| Default post-retirement return | 3.5% |
Key Assumptions
Every financial projection involves assumptions. Here are the key ones Isaac uses — all are adjustable in the app:
- Investment returns are applied as a constant annual rate, compounded monthly. Real-world returns vary year to year.
- Inflation is modelled as a constant rate. In practice, inflation fluctuates.
- Tax rates and bands use current legislation. Future governments may change these.
- State Pension is assumed to increase with inflation (triple lock approximation). The triple lock could be modified.
- Life expectancy is not modelled — projections run to age 100. You choose a target age for the solver.
- No investment fees are deducted by default. You can reduce your growth rate to account for fund charges.
- Annuity rates are user-specified, not market-linked. Actual rates at purchase will differ.
Important Disclaimer
Isaac is a planning tool, not financial advice. The projections are illustrative only and based on the assumptions you provide. Actual outcomes will differ due to market performance, inflation, tax changes, and personal circumstances.
Isaac is not regulated by the Financial Conduct Authority (FCA). For personalised financial advice, please consult a qualified Independent Financial Adviser (IFA).
Isaac is built and maintained by Budgetwise Limited (Company No. 15344334), trading as Isaac.