Compound Interest vs Simple Interest: How Each One Grows

Simple interest is calculated only on the amount you first deposit or borrow. Compound interest is calculated on that amount plus any interest already added to it, so each period's interest is a little larger than the last. Over a few months the two barely differ. Over many years the compounded balance pulls clearly ahead, which is good news for a saver and bad news for anyone carrying a debt that compounds.

The two formulas in plain words

With simple interest, the sum that earns interest never changes. Multiply the original amount by the rate and by the number of years, and you have the total interest. A loan of 1,000 at 5% simple interest for three years costs 150 in interest, 50 for each year, no matter what.

With compound interest, interest is added to the balance at set intervals, and from then on it earns interest too. The usual way to write it is:

• Final balance = starting amount × (1 + rate per period) raised to the number of periods.
• Rate per period = the yearly rate divided by how many times a year interest is added.
• Interest earned = final balance minus the starting amount.

Spreadsheets do this for you with a single formula, but it helps to see the numbers move by hand at least once.

A side-by-side example

Take 1,000 at a yearly rate of 5%, with compound interest added once a year. The figures below are plain arithmetic, rounded to two decimals, not a forecast of any real account.

In the first year nothing separates them. By year three the difference would barely buy a sandwich. By year twenty the compounded account has earned 1,653.30 in interest against 1,000.00 for the simple one, without a single extra deposit. Time does the work, which is why starting early matters more than most people expect.

How often interest is added

Compounding can happen yearly, quarterly, monthly or even daily. The more often interest is added, the sooner it starts earning, so the same headline rate produces a slightly higher result with more frequent compounding. The effect is modest at ordinary savings rates, yet it explains why two offers with the same quoted rate can end the year a little apart.

This is also why banks and lenders publish an annual equivalent figure alongside the nominal rate. Comparing those equivalent figures, rather than the headline numbers, puts accounts with different compounding schedules on the same footing.

Easy-access savings are where most households meet compounding first. Interest is often worked out on the daily balance and paid monthly, a pattern described in our piece on why high-interest savings accounts suit short-term money.

When compounding works against you

The same mechanism runs in reverse on debt. Unpaid interest on a credit card is typically added to the balance, and next month's interest is then charged on the larger sum. Leave a balance untouched and it grows on itself, just as a savings pot would.

Short-term property finance shows the borrower's side clearly. Some loans let interest be rolled up and settled at the end instead of paid monthly, which helps cash flow but means the amount owed keeps climbing until the loan is repaid. Our look at how bridging finance compares with a bank loan lists the questions about interest worth asking before signing.

• Ask whether interest is simple or compound, and how often it is added.
• Ask whether unpaid interest is capitalised, meaning it joins the balance.
• Compare the total repayable over the full term, not only the monthly figure.

A quick mental shortcut

The rule of 72 gives a rough idea of how long compound growth takes to double a sum: divide 72 by the yearly rate in percent. At 6%, money doubles in about twelve years; at 3%, in about twenty-four. It is an approximation that works best for moderate rates, but it is handy for sanity-checking a claim on the spot.

It also helps spot offers that sound too good. Anyone promising steady compounding at a high fixed rate with no risk deserves suspicion, and such pitches often arrive by email or text with a link attached. The checks in how to check if a link is safe are a sensible first step before clicking.

Points to keep in mind

Compounding only shows its strength when the money stays put; regular withdrawals interrupt it. Savings rates are usually variable, so the neat curve in a table rarely matches real life exactly. Inflation eats into what the final balance can buy, and interest may be taxable depending on where you live and the type of account. Investments that compound through reinvested returns can also fall in value, unlike a deposit at a fixed rate.

The figures here are illustrations of how the arithmetic works, not advice. For decisions about saving, borrowing or investing that matter to your household, a qualified independent adviser can look at your full situation.