How compound interest grows a savings account

Compound interest means interest is added to a balance, then later interest can be calculated on that larger balance. Your original deposit earns interest. Credited interest can earn interest too.

That second layer starts small. In the early years, new deposits usually do far more work than interest. Later, the interest line becomes more noticeable. The schedules below separate the two so you can see what is actually causing the growth.

What has to happen before interest can compound

The Australian government's Moneysmart explanation of compound interest distinguishes your starting balance, called principal, from interest already earned. Compounding happens when earned interest stays in the account and becomes part of a later interest calculation.

Three account terms control the result:

• the rate applied to the balance;
• how often interest is compounded;
• when interest is credited and available to earn further interest.

Calculation and crediting are not necessarily the same event. An account can calculate interest from each day's balance but add the accumulated amount to the account once a month. The savings-account interest guide walks through that daily ledger.

The compound-interest formula

For a single opening deposit, use:

A = P × (1 + r ÷ n)^(n × t)

Where:

• A is the estimated ending balance;
• P is the starting balance;
• r is the nominal annual rate written as a decimal;
• n is the number of compounding periods per year;
• t is the number of years.

The rate and the compounding period have to match. A monthly calculation calls for a monthly rate: divide a nominal annual rate by 12, with 12 periods in a year. An effective annual yield such as APY has already accounted for compounding, so dividing it by 12 would be wrong.

Schedule 1: one deposit left to grow

Suppose 5,000 stays in an account with a constant nominal annual rate of 4.8%, compounded monthly. There are no deposits, withdrawals, fees, taxes, rate changes, or account conditions in this illustration.

The monthly periodic rate is:

0.048 ÷ 12 = 0.004

After one year:

5,000 × (1 + 0.004)^12 = 5,245.35

The schedule continues like this:

Multiplying the first year's 245.35 by ten would give the wrong answer. Every interest credit raises the amount carried into the next calculation.

Schedule 2: a starting balance plus monthly deposits

Take a couple with 1,000 in the account who puts in another 200 at the end of each month, using the same sample rate. Their deposits add a second term:

ending balance = starting balance growth + deposit-stream growth

A = P × (1 + i)^N + C × [((1 + i)^N - 1) ÷ i]

In the formula, i means the rate per period, N means how many periods have passed, and C means each deposit.

Set i to 0.004 and the first 12 months look like this. We show cents here, but did not round the running calculation.

Over longer periods:

This schedule makes an easily missed point visible. At the end of year one, deposits supplied 3,400 of the 3,502.58 balance. Compounding added 102.58. The rate matters, but the couple's repeatable deposit did most of the early work.

If deposits arrive at the beginning of each month, each one gets an extra period of growth. If the dates or amounts vary, calculate the balance period by period instead of using the fixed-deposit shortcut.

APY and AER are annual comparison figures

In the United States, Regulation DD defines APY as the total interest paid over a 365-day period based on the rate and compounding frequency. The 4.8% nominal rate in the examples above becomes an APY of about 4.907% when compounded monthly:

(1 + 0.048 ÷ 12)^12 - 1 = 0.0490702

That APY describes the one-year effect of the stated rate and compounding assumptions. It is not an extra 4.907% paid on top of the nominal rate.

In the United Kingdom, the Financial Conduct Authority describes AER as an annual equivalent rate that takes account of compounding, bonuses, and charges. Other countries use different disclosure terms and rules. Use the annualized measure required where the account is offered, and compare figures under the same convention.

Why your statement will not match a clean schedule

The examples hold almost everything still. A real account does not.

Your result changes when:

• the rate is variable;
• a deposit arrives partway through a period;
• a withdrawal lowers the balance;
• the account uses balance tiers;
• a condition changes the rate earned;
• a fee is charged;
• interest is rounded or credited on a different schedule;
• local taxes apply.

The formula is an estimate until you replace every assumption with the current account terms. For product comparison, start with how high-yield savings accounts work and record the rate source and date.

A couple's growth ledger

If two people contribute different amounts or on different dates, do not let the interest calculation silently become a fairness rule. Track three lines:

PARTNER A DEPOSITS:
PARTNER B DEPOSITS:
HOUSEHOLD OR OTHER DEPOSITS:
INTEREST CREDITED:
WITHDRAWALS:
ENDING BALANCE:

The ledger answers what happened. It does not decide who should control the account or how a shared goal should be credited between partners.

Suppose one person can make the regular 200 deposit while the other handles a larger irregular household cost. The savings statement will show only the deposit. A useful money conversation names both contributions before discussing ownership or progress.

One way to open the conversation:

"Can we separate what we deposited from what the account earned, then decide whether our contribution plan still fits this month?"

For a real target and deposit schedule, use the shared savings goal calculator. Keep the calculator result as a planning estimate and compare it with the actual credited interest on each statement.