Compound Interest Explained: Worked Examples, the Rule of 72 and Fees

Compound interest is growth on growth: each year’s return is added to your capital, and next year’s return is earned on the larger sum. At 7% a year, 10,000 kronor becomes about 19,670 kronor in ten years and about 76,120 in thirty, against 31,000 with simple interest. Time does most of the work. Fees quietly undo it.

What is compound interest?

With simple interest you earn a return on your original sum only. With compound interest you also earn a return on every return already added. The formula is short: final amount = starting amount × (1 + rate) to the power of the number of years.

Take 10,000 kronor at 7% a year, with nothing added and nothing withdrawn:

For five years the two lines barely separate. After thirty, the compound account is worth more than twice the simple one. To check any figure yourself:

1. Write the rate as a decimal: 7% becomes 0.07.
2. Add one: 1.07.
3. Raise it to the number of years: 1.07 to the power of 10 is about 1.967.
4. Multiply by the starting sum: 10,000 × 1.967 = 19,670, close to the exact 19,672.
5. If fees apply, subtract them from the rate before step two.

One honest caveat. Shares do not pay a fixed rate. Real returns arrive unevenly, and the order matters: a gain of 50% followed by a loss of 50% does not leave you level. 100 becomes 150, then 75. The arithmetic of compounding still holds, but 7% here is an assumption for the maths, not a forecast.

The rule of 72: how long does it take to double your money?

Divide 72 by the yearly rate and you get a good estimate of the years needed to double. It works surprisingly well in the range most savers deal with.

The rule also works in reverse. The Riksbank’s inflation target is 2% a year; at that pace, prices double in roughly 35 years, and the purchasing power of cash left idle halves.

Time versus returns: why starting early wins

Compare two savers, each putting 12,000 kronor a year into the same investment, with 6% growth every year and deposits counted at the end of each year to keep the maths clean.

• Saver A pays in from age 25 to 35, then stops completely. Total paid in: 120,000 kronor. At 35 the account holds about 158,170. Left alone until 65, it grows to about 908,000.
• Saver B waits, then pays in from 35 to 65. Total paid in: 360,000 kronor. At 65 the account holds about 949,000.

Saver B paid in 240,000 kronor more and finished only about 40,000 ahead. Ten early years of saving did almost as much as thirty later ones. Swedes see the same principle in the premium pension, the part of the public pension invested in funds for decades before anyone draws on it.

How fees eat compound interest

Fees compound too, in the wrong direction. Invest 100,000 kronor for 30 years in two funds that both earn 7% a year before costs. One charges 0.2% a year, the other 1.5%. Treating the fee as a simple deduction from the return:

• At 6.8% net, the money grows to about 719,700 kronor.
• At 5.5% net, it grows to about 498,400 kronor.

The gap is about 221,300 kronor, almost a third of the larger sum, for a difference that looks trivial on a fact sheet. William Sharpe set out why this matters: before costs, the average actively managed krona must earn the market return, so after costs it must earn less. The same logic applies to the courtage you pay on every trade on Nasdaq Stockholm, explained in more depth in our guide to trading fees and commissions.

Tax can work like a fee as well. On an investment savings account (ISK), tax is based on a standardised yield calculated from the account’s value, not on your actual gains, so it behaves like a small yearly charge on the balance. The rate changes from year to year, and Skatteverket publishes the current rules.

Seeing compound growth in a game

Compounding is hard to feel when the payoff is decades away. A game compresses the timescale. In WallThrone you start with 25,000 dollars of play money, and the ranks are set by net worth: Known at 100,000, The Street at one million, then Player, Tower, Magnate and King, each ten times the last. Every step from The Street up asks for the same multiple, a little more than three doublings, whether you are climbing from one million or from a thousand million.

The costs compound as well. Every trade pays a commission of 0.05%. Trade your whole balance 200 times and about 9.5% of it is gone, since 0.9995 to the power of 200 is roughly 0.905. Traders you hire draw an hourly salary whether their trades win or lose, which is a fund fee in all but name. The prices come from the game’s own model and the companies are fictional, so the lesson is the arithmetic, not the returns.

Making compound interest work for you

• Start early, even small. The first years carry the most weight, as Saver A shows.
• Leave returns invested. Withdrawing gains resets part of the curve.
• Compare costs before returns. Past returns may not repeat; fees almost always do.
• Stay invested through bad years. Selling in a panic interrupts compounding at the worst moment, a habit rooted in the psychology of investing.

For neutral, free guidance on savings products, Konsumenternas Bank- och finansbyrå is a good first stop, and Finansinspektionen lets you check whether a firm is authorised.

Frequently asked questions

WallThrone is a free game played with play money and fictional companies; it is not a broker or an investment service. The examples above are arithmetic for learning, not forecasts or financial advice.