Interest

Interest is the price paid for the use of money over time. To a borrower it is the cost of having funds now rather than later; to a lender it is the return for parting with them and bearing the risk of not being repaid.

It is expressed as a rate — a percentage of an amount, per unit of time. The rate alone, however, says surprisingly little about what a loan costs. The same nominal rate can produce very different amounts depending on what it is calculated on, how often it compounds, and what fees sit alongside it. Those three variables are covered in detail on the pages linked below.

What makes up an interest rate

An interest rate is not a single price. It is a stack of components, each compensating the lender for something different.

ComponentWhat it compensates forReal risk-free rateThe pure time value of money — deferring consumptionInflation expectationErosion of purchasing power over the termCredit risk premiumExpected loss, given default probability and recoveryLiquidity and term premiumCapital being tied up, and uncertainty over longer horizonsOperating cost and marginOrigination, servicing, collection, capital cost and profit

An illustrative build-up for an unsecured loan in a moderate-inflation economy:

Real risk-free rate            3%
Expected inflation             8%
Credit risk premium            6%
Liquidity / term premium       2%
Operating cost and margin      7%
                             ────
Nominal rate                  26%

This is why rates that look high in one market can be unremarkable in another. Where inflation is 8% rather than 2%, every rate in the economy carries six extra points before any risk is priced. Comparing nominal rates across countries without adjusting for inflation is meaningless.

It also shows where a lender can and cannot compete. The first two components are set by the economy. The third depends on underwriting quality. Only the last is genuinely within a lender's control.

Simple and compound interest

Simple interest is calculated only on the original principal:

Interest = P × r × t

Compound interest is calculated on the principal plus accumulated interest:

Amount = P × (1 + r)^t

$1,000 at 10% per annum for 5 years:

Simple:    interest = $500.00    total = $1,500.00
Compound:  interest = $610.51    total = $1,610.51
Difference:                        $110.51

The gap widens sharply with time and rate. Over 20 years the same comparison gives $2,000 of simple interest against $5,727 compounded.

In lending practice, most instalment loans do not compound, because interest is paid each period rather than added to the balance. Compounding arises where interest is capitalised — during a payment holiday, on arrears, or on a deposit account.

The dimensions that determine what interest costs

Four variables change the amount payable at the same quoted rate. Each has its own page.

DimensionThe choiceEffectCalculation baseFlat vs reducing balanceFlat costs roughly 1.7–1.8× more at the same quoted rateCompounding frequencyNominal vs effectiveMore frequent compounding raises the true rateFee inclusionQuoted rate vs APRFees can add tens of percentage pointsAccrual basisDay count conventionChanges interest per period by 1–2%

A borrower comparing "18%" against "18%" without knowing these four answers is not comparing anything.

Fixed and variable rates

TypeHow it behavesWho bears rate riskFixedSet at inception, unchanged for the termThe lenderVariable / floatingReference rate plus a margin, resetting periodicallyThe borrowerCappedVariable, subject to a ceilingSharedHybridFixed for an initial period, then variableShifts at reset

Variable rates are quoted as a reference rate plus a margin — for example, "policy rate + 8%". Common references include the central bank policy rate, an interbank offered rate, or a published bank base or prime rate. When the reference moves, the borrower's rate moves with it, usually at defined reset dates.

Fixed rates give the borrower certainty and give the lender the risk. That risk is why fixed-rate loans often carry prepayment charges — the lender may have matched funding to the term and cannot simply unwind it.

Day count conventions

Interest per period depends on how days are counted.

ConventionMethod$100,000 at 10% for 30 daysActual/365Actual days ÷ 365$821.92Actual/360Actual days ÷ 360$833.3330/36030-day months ÷ 360$833.33

Actual/360 produces more interest than Actual/365 for the same rate, because the year is treated as shorter — which is why it persists in some money markets. 30/360 makes every month identical, simplifying schedules at the cost of slight inaccuracy.

The convention should be stated in the loan agreement. Where it is not, disputes over small differences in accrued interest are common and tedious.

Accrual, payment and capitalisation

Interest accrues continuously as time passes, but is paid periodically. Between payment dates, unpaid accrued interest is a real obligation — which is why a settlement figure taken mid-month exceeds the last statement balance.

Capitalisation is what happens when accrued interest is not paid and is instead added to the principal. From that point, interest is charged on the larger balance — the loan begins to compound.

Where it occurs:

• During a full payment holiday or moratorium
• On arrears, where the agreement provides for it
• In negative amortisation, where the instalment does not cover the interest accruing

Capitalisation is the mechanism that turns a manageable debt into an unmanageable one, because the balance grows while the borrower is paying nothing. It should always be disclosed explicitly, and borrowers should understand that a "payment holiday" is a deferral, not a waiver.

Interest in arrears and in advance

Most loans charge interest in arrears — the borrower has the money, then pays for having had it.

Discount instruments work the other way: interest is deducted up front and the borrower receives less than the face value. Treasury bills and discounted notes work this way.

Face value $10,000, 90 days, 10% discount rate
Discount   = 10,000 × 0.10 × 90 ÷ 365 = $246.58
Proceeds   = $9,753.42
True yield = 246.58 ÷ 9,753.42 × 365 ÷ 90 = 10.25%

The yield always exceeds the quoted discount rate, because the borrower never had the deducted amount to use.

Legal and religious limits

• Usury laws and rate caps. Most jurisdictions limit what may be charged, either as a general ceiling or by product. Caps on interest alone tend to push cost into fees, which is why fee-inclusive APR disclosure usually accompanies them.
• Islamic finance. Interest — riba — is prohibited. Financing is structured instead through profit-and-loss sharing, cost-plus sale (murabaha), leasing (ijara) and similar arrangements. These produce a return for the financier without charging interest on a loan, and are conceptually distinct from interest even where the cash flows resemble it.

Frequently asked questions

What is interest in simple terms? The price you pay for using someone else's money, or the return you earn for lending yours.

What is the difference between simple and compound interest? Simple interest is charged only on the original amount. Compound interest is charged on the original amount plus interest already accumulated, so it grows faster.

Does my loan compound? Usually not. On a standard instalment loan, interest is paid each period rather than added to the balance. Compounding happens when interest is capitalised — during a payment holiday or on arrears.

Why are interest rates higher in some countries? Largely because of inflation. Every rate in an economy carries an inflation component, so a 20% rate where inflation is 12% may be cheaper in real terms than an 8% rate where inflation is 2%.

What is the difference between a fixed and variable rate? A fixed rate stays the same for the term. A variable rate moves with a reference rate, so payments can rise or fall.

Why is my settlement figure higher than my last statement? Because interest has accrued since the statement date. Interest accrues daily even though it is billed periodically.

Is a lower interest rate always cheaper? No. What a loan costs depends on the calculation base, compounding, fees and term. Compare APR and total cost of credit rather than quoted rates.