Compound Interest Explained: $10,000 at 7% Becomes $76,123

A $10,000 deposit earning 7% a year grows to $76,123 in 30 years. With simple interest, which pays 7% of the original sum each year, the balance would be $31,000. The $45,123 difference is interest earned on interest.

Compound interest means interest that earns interest. Every figure here is arithmetic, with no market data. The 7% is an assumed round rate, not a forecast and not the average return of any fund or account.

Interest is the payment for letting someone use your money. The starting sum is the principal. Simple interest pays a fixed percentage of the principal each year. Compound interest pays a percentage of the principal plus all the interest added so far.

Our example sets the rules once. We deposit $10,000 on day one, add 7% interest at the end of each year, then leave everything in place. There are no further deposits, no tax and no fees.

Every figure below uses this setup unless the text says otherwise.

Of the $76,123, 13.1% is the original deposit and 27.6% is simple interest, the $700 a year the principal alone would earn. The remaining 59.3% is interest on interest, which is $45,123.

Chart 1 splits the balance by source at five-year steps. The deposit stays flat at $10,000. The simple interest grows in a straight line. The interest-on-interest segment starts small and then dominates.

At year 10 the interest-on-interest segment is $2,672 of a $19,672 balance. At year 20 it is $14,697 of $38,697. At year 30 it is $45,123 of $76,123.

Each year's interest is 7% of a bigger balance. Chart 2 shows the interest added each year.

Year 1 adds $700, the same as simple interest. Year 30 adds $4,980, which is 7.11 times as much.

Years 1 to 10 add $9,672. Years 11 to 20 add $19,025. Years 21 to 30 add $37,426, which is 3.87 times the first decade. It is 56.6% of the $66,123 of total interest.

The balance doubles every 10.24 years at 7%. It ends year 10 at $19,672, just below $20,000, then passes it in year 11 at $21,049. Each doubling adds more dollars than the one before, because it starts from a bigger sum.

The balance after t years is the principal P times (1 + r) to the power t, where r is the yearly rate written as a decimal. For 7%, r is 0.07.

After one year, $10,000 × 1.07 is $10,700. That year's interest is $700. After two years, $10,700 × 1.07 is $11,449, so year two adds $749. After 30 years, $10,000 × 1.07^30 is $76,123, which is 7.61 times the starting sum.

Simple interest has a different formula: P × (1 + r × t). It adds $700 every year, so 30 years gives $31,000.

A few percentage points of yearly rate change the result by multiples, not by small amounts. Chart 3 runs the same $10,000 for 30 years at five assumed rates.

The 9% balance of $132,677 is 3.07 times the 5% balance of $43,219. The 2 percentage points between 7% and 9% add $56,554, while the 2 percentage points between 5% and 7% add $32,903. The gap grows with the rate, because the extra interest compounds as well.

The same arithmetic works against a saver through costs.

We model a yearly cost as a cut in the rate of return, so a cost of 1 percentage point turns 7% into 6%. The 30-year balance falls to $57,435, which is $18,688 or 24.5% below the 7% result. Our explainer on what an index fund is covers how costs show up in a fund.

Time acts on the balance in the same way. The same $10,000 at 7% for 20 years instead of 30 reaches $38,697. The ten missing years cost $37,426. That is 49.2% of the 30-year balance.

Compound interest pays most at the end. The last ten of the 30 years produce more than the first twenty combined. Cutting off the end removes the largest part of the gain.

A rate can compound more than once a year. The nominal rate is the quoted yearly rate, here 7%. The compounding period is how often interest is added. The effective annual rate is the single yearly rate that gives the same result as the whole year of compounding.

With n periods a year, the balance becomes P × (1 + r / n)^(n × t). Each period earns r / n, so 7% compounded monthly earns 0.5833% a month.

$10,000 at a nominal 7% a year for 30 years, no deposits, tax or fees. Source: YX Insights

Monthly compounding lifts the 30-year balance from $76,123 to $81,165, which is 6.6% higher. Daily compounding reaches $81,645. Continuous compounding, the limit as the periods become infinitely small, reaches $81,662. The gain from more frequent compounding flattens quickly.

The example leaves out tax, because tax rules differ by account and country.

It also leaves out price rises. Suppose prices rise 3% a year for 30 years, an assumption chosen for the arithmetic. Prices would then be 2.43 times today's, so $76,123 would buy what $31,361 buys now.

Our explainer on how inflation erodes savings uses measured data.

The example also holds the rate fixed, while real returns vary.

Take $10,000 that rises 50% in year one to $15,000, then falls 50% in year two to $7,500. The mean of the two yearly returns is 0%. The money actually shrank by 13.4% a year, which is the compound rate. Our explainer on the compound rate against the average return covers that gap.

The example adds no money after day one. Our posts on investing $100 a month for 10 years and $500 a month for 20 years add regular deposits to the same arithmetic. Our first-portfolio guide covers what to hold.

Compound interest turned a $10,000 deposit into $76,123 in 30 years. Of that, $45,123 came from interest earned on earlier interest.

The Academy is free to read, here on the web. The Long Trend, our free weekly letter, comes by email.

This explainer is part of the YX Insights Academy. Each one takes a single idea and checks it against real data.

The same approach runs through everything else we publish:

Good places to start on the website:

Multiply the principal by (1 + r) raised to the number of years, where r is the yearly rate as a decimal. For $10,000 at 7% for 30 years, that is $10,000 × 1.07^30, which gives $76,123. Subtract the $10,000 principal to get the $66,123 of interest earned.

Money doubles in 10.24 years at 7% a year with interest added annually. In year-end balances, $10,000 is $19,672 after ten years and $21,049 after eleven.

For a saver, yes. Compound interest gives a larger balance than simple interest at the same rate after the first year. At 7% for 30 years, $10,000 gives $76,123 compounded and $31,000 with simple interest. For a borrower, the same arithmetic enlarges the debt.

Yes. At a 7% nominal yearly rate, monthly compounding turns $10,000 into $81,165 over 30 years, against $76,123 with yearly compounding. The effective annual rate rises from 7% to 7.229%. Daily compounding reaches $81,645, so the gain flattens as periods multiply.

DISCLAIMER: This article is intended for educational purposes only. Any information or analysis in this note does not constitute an offer to sell or a solicitation of an offer to buy any securities. Nothing in this note is intended to be investment advice, nor should it be relied upon to make investment decisions. Any opinions, analyses, or probabilities expressed in this note are those of the author as of the note's date of publication and are subject to change without notice.