Simple and compound interest, and why the gap grows
What actually differs between the two, why a quoted rate can mean several things, and what interest calculations routinely leave out.
One difference, and it is the whole thing
Simple interest is charged on the original amount only. Compound interest is charged on the balance, including interest already added. That is the entire distinction, and everything else follows from it.
Simple: A = P(1 + r·t) · Compound: A = P(1 + r/n)n·t
Over a single year at annual compounding the two give exactly the same answer, because there has been no opportunity for interest to earn interest yet. Beyond that they diverge — slowly at first, then not slowly at all.
On £10,000 at 5%, simple interest adds £500 every year forever. Compound interest adds £500 in year one, £525 in year two, £551 in year three. After ten years simple has produced £15,000 and compound £16,289. After thirty, simple gives £25,000 and compound £43,219 — nearly twice as much, from the same rate. The simple interest calculator shows the two side by side for exactly this reason.
Which one applies to you
This is not a choice; it is a property of the product.
Simple interest turns up in short-term notes, many bonds (where the coupon is paid out rather than reinvested), and some car and personal loans. The defining feature is that interest is calculated on the original principal and does not join the balance.
Compound interest governs savings accounts, mortgages, credit cards and investment growth. If interest is added to a balance that then earns further interest, it compounds — and the frequency of that addition matters.
The asymmetry worth internalising is that compounding is the same mechanism in both directions. It is the argument for starting to save early, and it is precisely why carrying a credit card balance is so punishing. A 22% card compounding monthly is not 22% a year; it is closer to 24.4%.
A quoted rate can mean several things
"5%" is ambiguous, and the ambiguity is worth money.
A nominal rate is the headline figure before compounding is accounted for. A effective rate is what you actually get once it is. Five percent nominal compounded monthly delivers 5.116% over the year, because each month's interest starts earning immediately.
Effective = (1 + r/n)n − 1
The gap widens with both the rate and the frequency. At 5% the difference between annual and monthly compounding is about a tenth of a percentage point; at 20% it is over a point and a half.
Regulators require comparable figures — APR for borrowing, AER or APY for saving — precisely because nominal rates are so easy to misread. When you enter a rate into any calculator, use the one your provider actually applies, and know which of the two it is. Entering an effective rate and then also selecting monthly compounding double-counts the effect.
The rule of 72, and when it stops working
Divide 72 by the annual percentage rate to get the approximate number of years to double. At 6%, twelve years; at 9%, eight.
It is a genuinely useful mental tool and it is an approximation. It is most accurate around 8%, drifts slightly low at very small rates and noticeably off above about 20%. At 6% the rule says 12 years and the exact answer is 11.9; at 30% it says 2.4 years against a true 2.64. Use it to sanity-check an order of magnitude, not to plan with.
What these calculations leave out
An interest calculation answers a narrow question precisely, and it is easy to mistake that precision for completeness. Three things are almost always absent unless a page says otherwise.
Tax. Interest is generally taxable, so a projection of what an account will hold overstates what you will keep. The effect compounds too: tax paid annually removes money that would otherwise have gone on earning.
Fees. Arrangement fees, monthly charges and early repayment penalties can reorder two offers that looked clearly ranked on rate alone. This is what APR exists to capture, and it is why comparing headline rates between products with different fee structures is misleading.
Inflation. A balance projected thirty years out is stated in today's money and will not buy today's basket. Nominal growth of 5% against 3% inflation is under 2% in real terms — most of the impressive-looking number is the currency changing rather than you getting richer. Theinflation calculator makes that adjustment separately, and it is worth doing for any long horizon.
Loans run the same maths backwards
A repayment loan is compound interest with payments working against it. Each payment covers the interest accrued since the last one, and whatever is left reduces the principal — which is why early payments are mostly interest and later ones mostly capital, on a schedule that has nothing to do with fairness and everything to do with the balance being larger at the start.
Two consequences follow. Overpaying early is worth far more than overpaying late, because it removes principal that would otherwise have accrued interest for the whole remaining term. And extending a term reduces the monthly payment while increasing the total paid, often substantially — a trade that is sometimes right and should always be made knowingly. Theloan calculator shows both the payment and the total interest so the comparison is visible.
Use these as planning tools
Every calculator here is arithmetic on assumptions you supply: a constant rate, regular contributions, no interruptions. Real accounts change their rates, real people miss a payment, and real products have terms that a formula does not model.
They are good for understanding the shape of a decision — whether a difference is worth caring about, how sensitive an outcome is to the rate, what an extra five years does. For anything with real money behind it, the agreement is the authority, and where the sums are significant it is worth paying someone qualified to read it.