Interest compounded daily refers to the method by which interest on a sum of money is calculated on a daily basis and then added to the principal sum. This means that the interest that is added to the principal on one day will earn interest on the next day, and so on.
This process of earning “interest on interest” is what makes compound interest grow at a faster rate than simple interest. You can read more about “The power of Compound Interest“.
The formula to calculate compound interest is:
A = P(1 + r/n)nt
Where
- A is the future value of the investment/loan, including interest.
- P is the principal investment amount (initial deposit or loan amount).
- r is the annual interest rate (as a decimal).
- n is the number of times interest is compounded per year.
- t is the time the money is invested or borrowed for, in years.
When interest is compounded daily: “n” = 365 (assuming 365 days in a year)
Example of interest Compounded Daily
Let’s assume:
Principal (P): $5,000 – This is the initial investment amount you started with.
Annual Interest Rate (r): 5% or 0.05
Number of compounding periods per year (n): 365 (daily compounding)
Time (t): 2 years
Now let’s see how much you will end up with at the end of the first year and at the end of the second year.
Year 1:
We will use this formula below to get the Future Value of the investment by the end of Year 1.
A1 = 5000(1 + 0.05/365)365×1
By the end of the first year, the future value of the deposit will be: $5,256.34.
The deposit grows from $5,000 to $5,256.34 by the end of the first year. This means you earned $5,256.34 − $5,000 = $256.34 in interest in the first year.
Year 2:
For Year 2, we will use the the formula below to get the Future Value of your investment at the end of Year 2.
A2 = 5000(1 + 0.05/365)365×2
By the end of Year 2, your total investment would have grown to $5,525.82.
The amount at the start of the second year is $5,256.34. By the end of the second year, it grows to $5,525.82. This means you earned $5,525.82 − $5,256.34 = $269.48 in interest in the second year.
The increased interest in the second year (compared to the first year) illustrates the effect of compounding: you’re earning interest not just on the original principal, but also on the interest earned during the first year.
Conclusion
In light of our example above, interest compounded daily plays a pivotal role in maximizing the growth potential of an investment or savings. Even over relatively short periods, such as the 2-year example we explored, the impact of daily compounding becomes evident.
This is why most financial advisors often emphasize the importance of starting to invest or save early. The benefits of daily compound interest become more pronounced over longer period 15+ years.
Besides daily compound interest, there are other compounding methods like Annually, Semi-Annually, Quarterly, and Monthly. Read More about “Compound Interest Frequencies“.
