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Tax-Aware Cash Lab · Methodology

How the calculation works

Compare the modelled after-tax outcomes from taxable savings, a Cash ISA, Premium Bonds and a directly held conventional gilt while keeping return type, uncertainty and maturity visible.

Return to calculator

Included

  • User-entered taxable savings and Cash ISA AERs
  • A marginal savings-income tax rate and unused annual allowance
  • Annual compounding and annual allowance use
  • The September 2026 Premium Bonds prize-fund rate, odds and estimated prize mix
  • 10,000 deterministic Premium Bonds simulations
  • Expected, median, percentile and no-prize outcomes
  • Every conventional gilt in the DMO issue dataset
  • User-entered clean price, accrued interest and dealing cost
  • Coupon tax and a CGT-exempt qualifying price-to-par gain
  • A maturity mismatch warning

Outside this method

  • A live best-buy or executable gilt-price feed
  • Product recommendations
  • Provider eligibility, credit quality and access-term checks
  • Full savings-income tax ordering
  • Automatic starting-rate-for-savings calculation
  • ISA subscription and transfer eligibility
  • FSCS-limit allocation
  • A formal gross redemption yield
  • The Accrued Income Scheme calculation
  • Index-linked gilts, funds and ETFs

Calculation

Core formulas

Taxable savings balance

Bᵧ = Bᵧ₋₁ + interestᵧ − max(0, interestᵧ − unused allowance) × tax rate

The entered AER and unused allowance are held constant and applied once in each whole modelled year.

Premium Bonds expected wins

λ = eligible £1 Bonds × eligible months ÷ 21,000

The published monthly odds produce the mean number of prizes under a Poisson approximation.

Premium Bonds expected value

Expected prizes = λ × weighted mean prize

The weighted mean uses NS&I's estimated September 2026 counts at every prize tier from £25 to £1 million.

Premium Bonds no-prize chance

P(no prize) = e^(−λ)

This is the zero outcome under the Poisson model for a fixed eligible holding.

Gilt nominal purchased

Nominal = (cash − dealing cost) × 100 ÷ (clean price + accrued interest)

The model spends the entered cash at the dirty price and then holds the conventional gilt to maturity.

Gilt after-tax value

Redemption nominal + remaining coupons − estimated coupon tax

A qualifying direct-gilt price gain is treated as exempt from CGT for a UK individual; coupons remain savings income.

Annualised net rate

(ending value ÷ opening cash)^(1 ÷ years) − 1

For the gilt, interim coupons are treated as if received at maturity, so the result is not a formal redemption yield.

Timing convention

When cash flows occur

Savings and ISA returns compound at each modelled year-end. Premium Bonds use whole eligible monthly draws and remove one draw for a new purchase. The direct gilt uses the DMO snapshot date to estimate remaining half-yearly coupons and runs to the actual maturity date, which can differ from the cash horizon.

Limitations

What the result cannot establish

  • Savings and ISA rates can change and products with the same headline rate can have different access conditions.
  • The annual unused-allowance input simplifies tax-year timing, other savings income and movement between tax bands.
  • Premium Bonds prize outcomes are highly skewed; 10,000 simulations cannot represent every rare-tail combination and do not predict a holder's result.
  • NS&I can change the prize-fund rate, odds and allocation after the stated effective date.
  • A gilt quote can include bid-offer friction and settlement details not captured by clean price, accrued interest and one fee.
  • Holding to maturity removes price uncertainty at the redemption date but not inflation, tax, reinvestment, issuer or forced-sale risk.

Reference tests

Numerical checks

CaseInputsExpected result
Taxable cash inside PSA£10,000; 5% AER; one year; £1,000 unused allowance; 20% rate£500 interest, £0 tax and 5% net rate
Higher-rate cash£50,000; 5% AER; one year; £500 unused allowance; 40% rate£2,500 interest, £800 tax and £1,700 net gain
Premium Bonds no-prize chance£1,000 holding; 12 eligible draws; 21,000-to-one monthly oddsApproximately 56.5% chance of no prize
Gilt at par without coupon£10,000 cash; £100 clean price; 0% coupon; £0 accrued interest and fees£10,000 redemption and £0 modelled gain

Evidence

Sources

HMRC — Tax on savings interest GOV.UK — 2026/27 savings rates and allowances NS&I — September 2026 Premium Bonds rate, odds and prize allocation NS&I — Premium Bonds key product information UK DMO — Gilts in Issue report HMRC — Gilt-edged securities exempt from Capital Gains Tax HMRC — Accrued Income Scheme