Simple vs Compound Interest: How the Gap Grows

How simple interest works

With simple interest the amount earned each year is always the same, because it is always calculated on the starting principal. The balance therefore rises by a fixed step each year, which is why the growth plots as a straight line.

interest = P × r × t total = P × (1 + r × t)P is the principal, r the yearly rate as a decimal, t the number of years.

Worked example: 5,000 at 4% for 10 years. The interest is 5,000 × 0.04 × 10 = 2,000, so the total is 7,000. That is 200 in every single year, which plots as a straight line.

How compound interest differs

With compound interest, each period's interest is added to the balance, so the next period starts from a larger base. For yearly compounding the total is P × (1 + r)^t.

Same example: 5,000 at 4% for 10 years, compounded yearly. The total is 5,000 × 1.04¹⁰ = 7,401.22, so the interest is 2,401.22. That is about 20% more interest than the simple version produced, from the same deposit and the same rate.

The first year looks identical: both methods pay 200, and the two totals agree after exactly one year. From then on the compound total is always the higher of the two. In the second year the compound version pays 208 because the balance is 5,200, and the extra amount keeps growing. For the full formula and a year-by-year table, see the compound interest formula, step by step.

Side by side over 40 years

Here is 5,000 at 4% under both methods, with yearly compounding for the second column:

After 5 years the gap is under 84, which is easy to ignore, and a short deposit period is the reason many people never notice the difference. After 30 years the compound interest earned (11,216.99) is nearly twice the simple interest (6,000). The simple total gains 200 every year; the compound total gains more each year than the year before.

The gap also widens with the rate. At the same 4%, time does most of the work; at a higher rate, the same pattern shows up much sooner.

Where you meet each type

• Savings and deposit accounts normally compound, often monthly or daily, though the terms vary by provider.
• Bonds typically pay a fixed coupon calculated on the face value, which behaves like simple interest unless you reinvest the payments.
• Short-term personal loans are sometimes described as simple interest. In that case interest is charged on the unpaid principal only, not on previously accrued interest. Because the principal falls as you repay, the interest charged each period falls too.
• Credit card balances that are not paid in full usually compound, which is why unpaid debt can grow quickly.

Worked example on the borrowing side: a 1,000 balance at 18% a year left untouched for 3 years. Simple interest would bring it to 1,000 × (1 + 0.18 × 3) = 1,540.00. Yearly compounding gives 1,000 × 1.18³ = 1,643.03. Monthly compounding, at 1.5% a month, gives 1,000 × 1.015³⁶ = 1,709.14. The same quoted rate costs more as the compounding gets more frequent.

Which one should you use in a calculation?

Use the method the product actually uses. If a contract says interest is added to the balance, use compound interest and match the compounding period. If it says interest is paid out and not reinvested, simple interest is the right model for that income, even if you later put the payments into something that compounds.

The compound interest calculator lets you set the compounding frequency, and the future value calculator is handy when you also add regular deposits.

This article is general education, not financial advice. Terms such as simple interest vary between lenders and countries, so read the actual agreement before you rely on a figure.