Methodology — savings & compound interest

1. Compound interest with monthly deposits

With monthly compounding and deposits made at the end of each month, the future value is:

FV = P·(1 + i)^N  +  C·[ ((1 + i)^N − 1) ÷ i ]

  P = starting amount
  C = monthly deposit
  i = monthly interest rate = (annual rate ÷ 100) ÷ 12
  N = number of months = years × 12

If i = 0:  FV = P + C·N   (no growth)

The first term compounds your opening balance; the second is the future value of an ordinary annuity — the stream of monthly deposits, each one compounding from the month it is paid in. Total paid in is P + C·N; interest earned is FV − (P + C·N).

2. Real (inflation-adjusted) value

To express a future balance in today’s purchasing power, it is deflated by inflation compounded over the same number of years:

Real FV = FV ÷ (1 + cpi/100)^years

  cpi = annual inflation rate (default: latest ONS CPI)

The real interest rate — whether savings beat inflation — is the nominal rate minus the inflation rate. At the current benchmark (3.75%) and CPI (2.8%) that is about 0.95 percentage points. This is an identity, not a prediction — it describes today’s rates, which change over time.

4. Assumptions & limits

• Interest is shown before tax; a taxed account grows a little slower (a cash ISA shelters interest from tax).
• The interest rate and monthly deposit are assumed constant for the whole term; real rates change.
• Interest is assumed to compound monthly; some accounts pay annually, which gives a slightly lower result.
• The Bank of England Bank Rate is an illustrative benchmark — it guides but does not set the rates providers offer, so enter your own rate for accuracy.
• Information only, not financial advice.