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103 LearnersLast updated on September 25, 2025
Daily Compound Interest Formula
Daily compound interest is essential in finance, as it calculates how much interest will be earned or paid on an investment or loan when it is compounded daily. In this topic, we will learn the formula for daily compound interest and how to apply it.
List of Formulas for Daily Compound Interest
The method for calculating daily compound interest involves specific formulas. Let’s learn the formula to calculate daily compound interest.
Formula for Daily Compound Interest
Daily compound interest is calculated using the formula:
A = P(1 + r/n)(nt)
Where: A = the future value of the investment/loan, including interest
P = the principal investment amount (initial deposit or loan amount)
r = the annual interest rate (decimal) n = the number of times that interest is compounded per year
t = the time the money is invested or borrowed for, in years
For daily compounding, n would be 365.
Importance of the Daily Compound Interest Formula
The daily compound interest formula is crucial in finance for accurately determining the future value of investments or the total loan amount.
It helps in:
- Calculating the amount of interest that will be earned or paid when interest is compounded daily.
- Planning investments and understanding the growth potential over time.
- Comparing different investment or loan options based on how interest is compounded.
Tips and Tricks to Memorize the Daily Compound Interest Formula
Some people find math formulas tricky and confusing.
Here are some tips and tricks to memorize the daily compound interest formula:
- Remember the acronym "PANDA" for Principal, Annual rate, Number of times compounded, Days, Amount.
- Visualize using different scenarios, such as loans or savings accounts.
- Use flashcards to memorize each part of the formula and practice rewriting it for quick recall.
Real-Life Applications of the Daily Compound Interest Formula
In real life, the daily compound interest formula plays a major role in finance.
Some applications include:
- Calculating the growth of savings accounts that offer daily compounding of interest.
- Understanding the total interest to be paid on loans that compound interest daily.
- Evaluating different investment opportunities based on how frequently interest is compounded.
Common Mistakes and How to Avoid Them While Using the Daily Compound Interest Formula
People often make errors when calculating daily compound interest.
Here are some mistakes and ways to avoid them.
Mistake 1
Not converting the interest rate to a decimal
Some may forget to convert the annual interest rate from a percentage to a decimal before using the formula.
To avoid this, divide the percentage by 100.
Mistake 2
Incorrectly identifying the number of compounding periods
Daily compounding means n should be 365, but some mistakenly use other values.
Always ensure n is set to 365 for daily compounding.
Mistake 3
Misunderstanding the time period
Confusion arises when t, the time in years, is incorrectly inputted.
Double-check the time period to ensure accurate calculations.
Mistake 4
Forgetting to apply the exponent
The formula involves raising the base to the power of nt.
Ensure you correctly apply the exponent to avoid errors.
Mistake 5
Mixing up principal and future value
It's crucial not to confuse P (principal) with A (future value).
Clearly differentiate between the starting amount and the amount after interest.
Examples of Problems Using the Daily Compound Interest Formula
Problem 1
Calculate the future value of a $2,000 investment with an annual interest rate of 4% compounded daily for 3 years.
The future value is approximately $2,247.91
Explanation
Using the formula
A = P(1 + r/n)^(nt):
P = $2,000, r = 0.04,
n = 365, and t = 3
A = 2000(1 + 0.04/365)^(365*3)
A ≈ $2,247.91
Problem 2
Find the amount to be paid on a $1,500 loan with an annual interest rate of 5% compounded daily over 2 years.
The amount to be paid is approximately $1,660.22
Explanation
Using the formula
A = P(1 + r/n)^(nt):
P = $1,500, r = 0.05,
n = 365, and t = 2
A = 1500(1 + 0.05/365)^(365*2)
A ≈ $1,660.22
Problem 3
Determine the future value of a $5,000 deposit with a 3% annual interest rate compounded daily for 5 years.
The future value is approximately $5,808.08
Explanation
Using the formula
A = P(1 + r/n)^(nt):
P = $5,000, r = 0.03,
n = 365, and t = 5
A = 5000(1 + 0.03/365)^(365*5)
A ≈ $5,808.08
Problem 4
What will be the future value of $3,000 invested at 6% interest compounded daily for 4 years?
The future value is approximately $3,834.35
Explanation
Using the formula
A = P(1 + r/n)^(nt):
P = $3,000, r = 0.06,
n = 365, and t = 4
A = 3000(1 + 0.06/365)^(365*4)
A ≈ $3,834.35
Problem 5
Find the future value of a $10,000 investment with a 2% annual interest rate compounded daily for 1 year.
The future value is approximately $10,201.34
Explanation
Using the formula
A = P(1 + r/n)^(nt):
P = $10,000,
r = 0.02,
n = 365, and t = 1
A = 10000(1 + 0.02/365)^(365*1)
A ≈ $10,201.34
FAQs on Daily Compound Interest Formula
1.What is the formula for daily compound interest?
2.How is daily compounding different from annual compounding?
3.How do I convert the annual interest rate to a decimal?
4.What does 'n' represent in the formula?
5.Why is it important to understand the compounding frequency?
Glossary for Daily Compound Interest Formula
- Principal: The initial sum of money invested or loaned.
- Future Value: The amount of money an investment will grow to over time with interest.
- Compounding Frequency: How often interest is added to the principal.
- Annual Interest Rate: The percentage of interest earned or paid over a year.
- Exponential Growth: The increase in value at a consistent rate over time, characteristic of compound interest.
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Jaskaran Singh Saluja
About the Author
Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.
Fun Fact
: He loves to play the quiz with kids through algebra to make kids love it.
