How Compound Interest Works: The Maths Behind the Calculator

Compound interest is interest calculated on both the initial principal and the accumulated interest from previous periods. Unlike simple interest — which only earns on the original amount — compound interest accelerates growth exponentially over time. This is why Albert Einstein reportedly called it “the eighth wonder of the world.”

The formula is: A = P(1 + r/n)^(nt) — where A is the final amount, P is the principal, r is the annual interest rate, n is how often interest compounds per year, and t is time in years. Most investment platforms compound either daily or monthly.

What Does 7% Annual Return Actually Mean for UK Students?

The calculator defaults to 7% — a commonly cited long-run average for a globally diversified equity index fund (such as the FTSE All-World or MSCI World) after adjusting for inflation. This is a reasonable starting assumption, but not a guarantee. Actual returns vary year-to-year and depend on which funds you hold. UK Cash ISAs currently offer around 4–5% AER (June 2026, Bank of England base rate at 3.75%), making the gap between cash savings and equity investing highly visible in the calculator over longer timeframes.

Three Things the Calculator Shows That Most Students Ignore

1. Starting earlier matters more than investing more. Increasing the time period from 10 to 20 years has a larger effect on the final value than doubling your monthly contribution at the 10-year mark. Time is the most powerful variable in the equation.
2. Small monthly contributions compound dramatically. A student who invests just £30/month for 40 years at 7% ends up with over £78,000 — despite only contributing £14,400 in total. The remaining £64,000 is pure compound growth.
3. The ISA wrapper eliminates the tax drag. Outside an ISA, gains above the £3,000 Capital Gains Tax annual exempt amount (2026/27) are taxable. Inside a Stocks and Shares ISA, all growth is tax-free. This materially increases the effective return shown by the calculator for UK investors.

Frequently Asked Questions

What interest rate should I use for UK savings accounts?

For Cash ISAs and easy-access savings, use 4–5% AER as a realistic 2026 figure. For fixed-rate bonds (1–2 year), rates of 4.5–5.2% are available. For equity index funds (long-term, 10+ years), 6–8% real return is a widely used planning assumption, though past performance is not a guide to future results.

How often does interest compound on UK investment platforms?

Most UK investment platforms (Trading 212, Vanguard, InvestEngine) accrue returns continuously as markets move rather than applying discrete compound periods. For Cash ISAs and savings accounts, interest typically compounds either monthly or annually — check the AER vs gross rate on your account to see the difference.

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