Written byCompound interest is interest calculated on both the original principal and the interest already added in earlier periods, so balances and debts grow faster than with simple interest.
Also known as: compounding, interest on interest, compounding interest
Key points
- At the end of each period, interest is added to the balance and the new, larger balance earns interest in the next period.
- It grows savings, term deposits and superannuation, and it adds to the cost of loans, mortgages and credit cards.
- The more often interest compounds (daily rather than yearly), the higher the effective return or cost for the same nominal rate.
- The effective annual rate (EAR) includes compounding, so it is the figure to compare rather than the nominal rate alone.
How compound interest works
Start with a principal P, the amount deposited or borrowed. Apply an annual nominal interest rate r, expressed as a decimal, and choose a compounding frequency n: yearly, quarterly, monthly or daily. At the end of each compounding period, interest is calculated and added to the balance, and that new balance becomes the principal for the next period. In plain English, the balance grows by a factor of (1 + r/n) every period, and over many periods that growth multiplies.
The standard formula with no regular contributions is A = P(1 + r/n)^(nt), where A is the final balance and t is the number of years. With regular contributions, add an annuity term: the contribution multiplied by ((1 + r/n)^(nt) - 1) divided by (r/n). Simple interest, by contrast, is worked out on the original principal only, so each period earns the same amount.
Compounding frequency and the effective rate
For a given nominal rate, more frequent compounding produces a slightly higher final balance. The differences are modest at low rates but grow with higher rates and long horizons. Banks commonly compound daily or monthly on savings and mortgage interest, so check the account terms and conditions, or the credit contract, to see how interest is calculated and credited.
Because a quoted nominal rate does not show compounding, the effective annual rate (EAR) is the better comparison figure: EAR = (1 + r/n)^n - 1. Continuous compounding, A = Pe^(rt), is the theoretical limit as n heads to infinity; it is useful in finance theory but everyday accounts use daily or monthly compounding.
Where it works for you and against you
Compounding works for you when you save. Many savings accounts compound daily and credit interest monthly, term deposits are quoted as a fixed rate for the term with compounding that depends on the product, and superannuation earnings compound over decades on top of regular contributions. Starting early, contributing regularly and reinvesting returns all enlarge the base that compounds, while fees shrink it. Interest income is generally assessable, so tax and inflation reduce the real return.
It works against you with debt. On mortgages and personal loans, compounding and repayment frequency change the total cost, and on credit cards interest is commonly calculated daily on the outstanding balance, so unpaid balances can escalate quickly. Compounding also affects repayments and residuals in equipment finance, which is worth knowing when comparing a finance lease or novated lease.
Example
A saver puts money away for ten years at a fixed rate, with interest added once a year. Under simple interest the account earns the same amount every year, because the calculation always goes back to the original deposit. Under compound interest, year two's interest is worked out on the deposit plus year one's interest, year three's on that larger balance again, so the account finishes higher. That difference is the interest on interest. Compounding monthly or daily instead of yearly widens it again, and the longer the term, the wider the gap gets. Moneysmart's compound interest calculator does the arithmetic on your own numbers.
Not to be confused with
- Simple interest
- simple interest is calculated on the original principal only, so it never earns or charges interest on interest
- Nominal rate
- the nominal rate is the quoted annual rate before compounding; compounding is why the effective annual rate ends up higher
Frequently asked questions
What is the difference between compound interest and simple interest?
Simple interest is calculated only on the original principal, so every period earns or charges the same amount. Compound interest is calculated on the principal plus the interest already accumulated, so the amount grows each period. Over long terms the difference becomes large, which is why compounding is described as exponential growth.
How do you calculate compound interest?
Use A = P(1 + r/n)^(nt): P is the starting amount, r the annual nominal rate as a decimal, n the number of compounding periods a year and t the number of years. A is the final balance, and interest earned is A minus the amount put in. Moneysmart's compound interest calculator does the arithmetic for you.
How often is interest compounded on savings accounts and loans?
Many savings accounts compound daily and credit the interest monthly. Home loan interest is also commonly calculated daily, and credit card interest is usually calculated daily on the outstanding balance. Term deposits vary by product. The account terms and conditions, or the credit contract, set out exactly how interest is calculated and credited.
What does effective annual rate (EAR) mean?
The effective annual rate is the annual return or cost once compounding is included, calculated as (1 + r/n)^n minus 1. A nominal rate compounded monthly produces a slightly higher effective rate than the same rate compounded yearly, which is why comparing effective rates is more accurate than comparing nominal rates.
Does compound interest apply to loans as well as savings?
Yes. On a loan, compounding increases what you owe whenever interest is capitalised, meaning added to the balance rather than paid. Repayment frequency matters too, because paying more often reduces the balance that interest is calculated on. Credit cards and payday loans often compound frequently, so small unpaid balances can grow quickly.
Related terms
Broader term: Interest
Interest
Interest is the price of using money: what a borrower pays on a loan, or a saver earns on a deposit, expressed as a percentage rate on the principal.
Read definitionSimple interest
Simple interest is interest calculated only on the original principal, never on interest already added, which keeps the charge flat across the term.
Read definitionNominal rate
A nominal rate is the headline annual interest rate a lender quotes before compounding within the year is taken into account, unlike the effective annual rate.
Read definitionPrincipal
Principal is the amount of money you originally borrowed or, on a running loan, the part of that sum you still owe, excluding interest, fees and charges.
Read definitionComparison rate
A comparison rate is a single annual percentage that combines a loan's interest rate with most upfront and ongoing fees to show its ongoing cost more clearly.
Read definitionFixed rate
A fixed rate is an interest rate locked in for a set term, so the rate and usually the repayments do not change until that term ends.
Read definitionGo deeper
Sources
This article is general information only and is not financial advice.