How Compound Interest Is Calculated Annually, Daily and Continuously
The basic concept of interest is really straightforward. If you have $10,000 in an investment and it earns 10% interest compounded annually, you’ll earn $1,000 in interest in a year. It’s easy — it’s just 10% of $10,000.
Yet, if you try to apply that type of simple math to your credit cards or to other types of investments, you might find that the numbers don’t come out quite as you expect.
For example, let’s say you look at a credit card with a $10,000 balance and a 30% APR. You might think that your credit card would accumulate $3,000 in interest over the course of a year, but you’d be wrong. Leave that card untouched for a year and you’ll face $3,496.92 in interest.
Where did that extra $500 in interest come from? It’s all about the compound interest, and it’s much easier to understand if you break it down step by step.
What is compound interest?
Compound interest is the addition of a sum to the original balance, whether it be an investment, deposit or a principal loan amount.
In our earlier example, your initial $10,000 earns 10% in interest, giving you a new balance of $11,000 after the first year.
After the second year, your $11,000 earns 10% in interest, giving you a new balance of $12,100.
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After the third year, the same thing happens again — your $12,100 earns 10% in interest, growing your total investment to $13,310. After the fourth year, your investment grows to $14,641. After 10 years you’ll have $25,937.42.
This reveals a powerful core principle: the more frequently something compounds, the faster your investment — or the interest you owe — will grow. When you’re investing, faster compounding is better. When you’re paying interest, slower compounding is better.
How is credit card interest calculated?
Most credit card issuers compound interest daily. This means that each day, interest is calculated on your balance for that day. Purchases made on your card don’t immediately start earning interest, but when they do, it’s calculated daily.
Credit card issuers usually describe interest rates as an APR. Suppose you have a credit card with a 36.5% APR. Since your credit card compounds daily, your credit card issuer will calculate 1/365 of that annual interest rate each day and then add that onto your balance. (Note that some financial institutions use 1/360 instead, for easier calculation.)
If you have a card with a 36.5% APR, each day you’re getting charged 1/365 of that — 36.5% multiplied by 1/365 is 0.1%.
Now, let’s say you have a credit card balance of $1,000. On the first day, it accrues $1,000 times 0.1% in interest — or $1. However, your balance is now $1,001. On the next day, it accrues $1.001 in interest. That makes your new balance $1,001.001 (yep, a fraction of a cent). Your credit card company is going to keep track of those fractions because over time, it adds up to pennies, dimes and dollars. Credit card issuers usually calculate down to the thousandths of a cent.
Over time, that little fraction grows. After 30 days of daily compounding at 0.1%, your $1,000 has become $1030.44, rounded to the nearest penny.
What about over the course of a year? If you owe $1,000 and you’re paying 36.5% interest compounded annually, you’d owe $1,365 at the end of the year. If it’s compounded daily, it’ll add up to $1,440.25. Those little fractions of a cent can really add up.
What is continuous compound interest?
Occasionally, you’ll find a financial institution using continuous compound interest — while rare, it can happen. In practice, continuous compound interest ends up earning just slightly more than daily compound interest — about 1% more over the course of a year.
Continuous compound interest means that there aren’t compounding periods — it’s compounding all the time. With annual compounding, you calculate interest once a year. With daily compounding, you calculate it once a day. With constant compounding, you calculate it constantly.
The math behind continuous compound interest is trickier. If you want an approximate of your continuous compound interest, you can calculate the daily compound interest with an interest rate 1% higher than the actual rate — you’ll get very close to the number.
How does compound interest affect my finances?
To put it simply, when borrowing money, you want interest compounded less frequently. Conversely, when investing money, you want interest compounded more frequently. Financial institutions want the opposite — they want to compound more frequently on the money they lend you, and less frequently on the money you deposit.
Financial institutions usually state the interest rate on money loaned to you as an APR. APR is the annual percentage rate, but it doesn’t tell you how often the interest is compounded. Generally, banks compound this amount daily on the money they lend out, so the actual interest you’d pay out in a year is more than the APR might have you believe. As we saw earlier, the $1,000 borrowed at 36.5% APR would turn into $1,365 if compounded annually, but $1,440.25 if compounded daily.
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On the other hand, financial institutions usually state the interest rate on money you deposit with them as APY — the annual percentage yield — which is how much your money would actually grow in a year, regardless of how frequently it’s compounded
If a bank says you have 1% APY on a savings account, it could mean that the institution is offering a 1% APR savings account that compounds once a year, a 0.995% APR savings account that compounds quarterly or a 0.99% APR savings account that compounds monthly. They will all earn you 1% on your money if you leave it there for a full year.
The only difference is what happens if you withdraw that money early. If you take it out after seven months, you’ll have earned money in the monthly and quarterly compounding accounts, but not the annual compounding account. If you take it out after two months, the quarterly compounding account won’t earn you anything.
At very low interest rates, like the rates we have today, it’s a minor factor — usually adding up to just a few cents. Nonetheless, when rates are high, it can make a significant difference.
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