Compound Interest Calculator
What is Compound Interest? | Compound Interest Explained
Compound interest is one of the most powerful concepts in finance. Unlike simple interest, which is calculated only on the principal amount, compound interest allows your money to grow exponentially by earning interest on both the principal and previously earned interest.
Simple Interest vs Compound Interest
Simple Interest is calculated only on the original principal:
Interest=Principal×Rate×Time\text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time}
For example, borrowing $100 at a 10% simple interest rate for 2 years:
$100×10%×2=$20\$100 \times 10\% \times 2 = \$20
Compound Interest, on the other hand, is calculated on the principal plus accumulated interest. Using the same example:
End of Year 1: $100 × 10% = $10 → Balance = $110
End of Year 2: $110 × 10% = $11 → Total = $121
Key takeaway: Compound interest earns more over time because interest itself generates interest.
Why Compound Interest Matters
Compound interest works like a snowball, growing your money faster with time. It can be a double-edged sword:
For investors, it accelerates wealth growth
For borrowers, it increases total debt if left unpaid
Example: A 20-year-old invests $1,000 in the stock market at an average 10% annual return. By age 65, this investment could grow to $72,890, nearly 73 times the initial amount!
Compounding Frequency
The frequency of compounding affects how much interest accrues:
Annually: Interest is added once per year
Semi-annually: Added twice a year
Monthly or Daily: Added monthly or daily, increasing total interest
Example: $100 at 10% interest, compounded semi-annually:
First 6 months: $100 × 5% = $5
Next 6 months: ($100 + $5) × 5% = $5.25
Total interest = $10.25 → slightly higher than annual compounding
Savings accounts, CDs, and mortgages often use different compounding frequencies.
Compound Interest Formula
1. Standard Compounding:
At=A0(1+r)nA_t = A_0 (1 + r)^n
Where:
A0A_0 = principal amount
AtA_t = amount after n periods
rr = interest rate per period
nn = number of compounding periods
Example: $1,000 at 6% annual interest for 2 years:
At=1000×(1+0.06)2=1123.60A_t = 1000 \times (1 + 0.06)^2 = 1123.60
2. Compounding Multiple Times a Year:
At=A0(1+rn)nâ‹…tA_t = A_0 \left(1 + \frac{r}{n}\right)^{n \cdot t}
Where nn = number of compounding periods per year.
Example: $1,000 at 6% interest, compounded daily:
Daily rate = 6% ÷ 365 ≈ 0.0164384%
After 2 years:
At=1000×(1+0.000164384)365⋅2≈1127.49A_t = 1000 \times (1 + 0.000164384)^{365 \cdot 2} \approx 1127.49
Continuous Compounding
Continuous compounding represents the mathematical limit of compound interest as the number of periods becomes infinite:
At=A0ertA_t = A_0 e^{r t}
Example: $1,000 at 6% annual interest, compounded continuously for 2 years:
At=1000×e0.06×2≈1127.50A_t = 1000 \times e^{0.06 \times 2} \approx 1127.50
Rule of 72
The Rule of 72 is a quick way to estimate how long it takes to double an investment:
Years to double=72Interest Rate (%)\text{Years to double} = \frac{72}{\text{Interest Rate (\%)}}
Example: $100 invested at 8% annual return → 72 ÷ 8 = 9 years to double
Note: The Rule of 72 is an approximation, useful for quick mental calculations.
History of Compound Interest
Compound interest has been used for over 4,400 years by Babylonians and Sumerians.
Initially, it was considered usury in many societies, including Roman law and some religious texts.
Modern compound interest became widely used in the 1600s with the creation of interest tables.
Jacob Bernoulli and Leonhard Euler formalized the concept of continuous compounding using the mathematical constant e ≈ 2.71828.
Why Use a Compound Interest Calculator
A compound interest calculator simplifies:
Calculating future value of investments
Comparing daily, monthly, or annual compounding
Planning for retirement, savings, or loans
Understanding the effect of interest on debt