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 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.

• Real risk-free rate: The pure time value of money — deferring consumption
• Inflation expectation: Erosion of purchasing power over the term
• Credit risk premium: Expected loss, given default probability and recovery
• Liquidity and term premium: Capital being tied up, and uncertainty over longer horizons
• Operating cost and margin: Origination, 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.

• Calculation base (Flat vs reducing balance): Flat costs roughly 1.7–1.8× more at the same quoted rate
• Compounding frequency (Nominal vs effective): More frequent compounding raises the true rate
• Fee inclusion (Quoted rate vs APR): Fees can add tens of percentage points
• Accrual basis (Day count convention): Changes 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

• Fixed: Set at inception, unchanged for the term (Rate risk borne by: Lender)
• Variable / floating: Reference rate plus a margin, resetting periodically (Rate risk borne by: Borrower)
• Capped: Variable, subject to a ceiling (Rate risk borne by: Shared)
• Hybrid: Fixed for an initial period, then variable (Rate risk borne by: Shifts 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.

• Actual/365: Actual days ÷ 365 ($821.92 on $100,000 at 10% for 30 days)
• Actual/360: Actual days ÷ 360 ($833.33 on $100,000 at 10% for 30 days)
• 30/360: 30-day months ÷ 360 ($833.33 on $100,000 at 10% for 30 days)

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.