Compound Interest vs Simple Interest: The $1,000 Example That Shows the Difference

Put $1,000 in an account at 7% for 30 years. With compound interest you end with $7,612.26. With simple interest you end with $3,100.00. Same starting amount, same rate, same 30 years — a difference of $4,512.26, and the gap grows every single year. That is the whole difference between the two kinds of interest, in one example.

Simple interest pays only on the original amount. Compound interest pays on the original amount plus all the interest earned so far. This guide runs the same $1,000 through both formulas at 5%, 6% and 7%, shows the year-by-year gap, explains when each type is actually used, and covers the mistakes that mix them up.

The Two Formulas, Side by Side

Simple interest: A = P(1 + r × t). The interest is always 7% of $1,000 = $70.00 a year, so 30 years gives $2,100.00 of interest and A = $3,100.00.

Compound interest: A = P(1 + r)^t (annual compounding). The interest is 7% of the current balance: $70.00 in year 1, $128.69 in year 10, $253.16 in year 20, $498.00 in year 30. Total interest: $6,612.26, so A = $7,612.26.

The difference is one idea: in the simple formula the balance never changes, so the yearly interest never changes; in the compound formula the balance is last year’s balance, so the yearly interest grows with it. Calcrio’s free compound interest calculator gives the compound future value with the full year-by-year table — subtract P(1 + r × t) to see the gap for any inputs.

The $1,000 Example, Year by Year

After 1 year the two answers are identical — $1,070.00 either way — because no interest has had a chance to earn interest yet. The gap opens slowly, then explodes: $52.55 after 5 years, $267.15 after 10, $1,469.68 after 20, and $4,512.26 after 30, when the compound balance is nearly two and a half times the simple one.

The same pattern holds at lower rates — the gap is smaller, but it still accelerates:

Two lessons: the gap grows far faster than the time does — at 7% it goes $267.15 → $1,469.68 → $4,512.26 — and the rate matters as much as the time: at 5% for 30 years the gap is $1,821.94, but at 7% it is $4,512.26.

Why the Gap Widens Every Year

The yearly interest under simple interest is a flat $70.00 — draw it on a chart and it is a horizontal line. The yearly interest under compound interest is 7% of a growing balance, so it is a curve bending upward: $70.00 in year 1, $91.76 in year 5, $128.69 in year 10, $253.16 in year 20, $498.00 in year 30. The gap between the two balances in any year is exactly the sum of all the extra yearly interest so far — the interest earned on interest that simple interest never pays.

When Is Each Type Actually Used?

Compound interest is the default for savings accounts, certificates of deposit, investment growth and credit-card debt — anywhere a balance carries forward. Your savings account compounds (usually monthly or daily); your investment portfolio compounds when returns are reinvested; and a credit card compounds against you, which is why a balance left unpaid grows so fast.

Simple interest shows up in short-term loans, some auto loans and Treasury bills, where the term is short or the interest is calculated once on the original amount. The practical rule: if the interest stays in the account, it compounds; if it is paid out each period, it is simple. Reinvested dividends compound the same way — the SCHD dividend calculator shows a reinvested yield snowballing exactly like the $1,000 example.

3 Mistakes That Mix Them Up

1. Using P(1 + rt) when the question says “compounded”. The word “compounded” always means the compound formula; P(1 + rt) is only for simple interest. On $1,000 at 7% for 30 years, the wrong formula gives $3,100.00 instead of $7,612.26 — an error of $4,512.26.

2. Adding the interest once instead of every year. A common wrong answer is $1,000 + $70.00 = $1,070.00 — one year of interest, not thirty. Simple interest adds $70.00 every year, 30 times; compound interest adds a growing amount every year.

3. Forgetting that the first year is identical. If your compound and simple answers differ after 1 year, one is wrong — both give $1,070.00 after one year at 7%. The difference only appears from year 2 onward.

Frequently Asked Questions

What is the difference between compound and simple interest?
Simple interest is calculated only on the original principal: A = P(1 + rt). Compound interest is calculated on the principal plus all interest earned so far: A = P(1 + r)^t. On $1,000 at 7% for 30 years: $7,612.26 vs $3,100.00.

Which is better, compound or simple interest?
For saving, run the numbers in a compound interest calculator — compound interest is far better, because it pays interest on the interest. For borrowing, simple interest is cheaper. The $1,000 example shows the saver’s side: $4,512.26 extra over 30 years at 7%.

How much more is compound interest than simple interest on $1,000 at 7% for 10 years?
$267.15 more: $1,967.15 compound vs $1,700.00 simple. After 20 years the gap is $1,469.68; after 30 years, $4,512.26.

Do banks use compound or simple interest?
Savings accounts and investments compound (usually monthly or daily). Some short-term loans use simple interest. Always check the frequency: $1,000 at 5% for 10 years is $1,628.89 annually but $1,647.01 monthly.

Why are compound and simple interest the same after 1 year?
Because after one year no interest has had time to earn interest yet. Both formulas give P(1 + r): $1,000 at 7% is $1,070.00 either way. The difference starts in year 2.

Keep Practicing

Work these by hand: $1,000 at 6% for 20 years is $3,207.14 compound vs $2,200.00 simple (gap $1,007.14); $500 at 7% for 30 years is $3,806.13 vs $1,550.00 (gap $2,256.13 — exactly half the $1,000 gap, because the gap scales with the principal). For instant answers, use the free compound interest calculator — and for the most famous compounding example of all, the how long does $100 take to become $1,000 guide works through the 34-year journey: $997.81 after 34 years, $9,956.27 after 68.