David is a Chartered Financial Analyst with over 15 years of experience in financial planning and investment analysis, specializing in modeling portfolio growth and long-term returns.
This 4-in-1 Compound Interest calculator helps you plan your financial future. Enter any three values—Future Value, Principal Amount, Annual Rate, or Term—and we will solve for the fourth.
Compound Interest Calculator
Compound Interest Formula (Annual)
A = P * (1 + R)^T
Solve for Principal (P):
P = A / (1 + R)^T
Solve for Rate (R):
R = (A / P)^(1 / T) – 1
Solve for Term (T):
T = log(A / P) / log(1 + R)
Formula Variables
- (A) Future Value: The total value of the investment or loan at the end of the term, including all accumulated interest.
- (P) Principal Amount: The initial amount of money invested or borrowed.
- (R) Annual Rate: The annual interest rate as a decimal (e.g., 5% = 0.05). This calculator assumes compounding once per year.
- (T) Term: The total number of years the money is invested or borrowed for.
Related Calculators
- Simple Interest Calculator for Loans
- Investment Property Calculator
- Savings Goal Calculator
- 401k Loan Calculator
What is Compound Interest?
Compound interest is the “interest on interest” that allows an investment to grow at an accelerating rate. Unlike simple interest, which is calculated only on the original principal, compound interest is calculated on the principal *plus* all previously accumulated interest.
For example, if you invest $1,000 at 10% annual compound interest:
• Year 1: You earn $100 ($1,000 * 10%). Your new balance is $1,100.
• Year 2: You earn $110 ($1,100 * 10%). Your new balance is $1,210.
• Year 3: You earn $121 ($1,210 * 10%). Your new balance is $1,331.
This exponential growth is why Albert Einstein reportedly called compound interest the “eighth wonder of the world.” It is the fundamental concept behind long-term investing, retirement savings, and also the reason why high-interest loan balances can grow so quickly.
How to Calculate Compound Interest (Example)
-
Identify the Variables
Let’s say you want to invest for retirement. The details are:
• Principal (P): $25,000
• Annual Rate (R): 7%
• Term (T): 20 years
We need to find the Future Value (A). -
Choose the Correct Formula
To find the Future Value, we use the formula:
A = P * (1 + R)^T -
Convert the Rate
First, convert the annual percentage rate (R) from a percentage to a decimal:
R = 7% / 100 = 0.07 -
Calculate the Future Value
Now, plug the values into the formula:
A = $25,000 * (1 + 0.07)^20
A = $25,000 * (1.07)^20
A = $25,000 * 3.86968
A = $96,742.11
Your investment would grow to $96,742.11 over 20 years.
Frequently Asked Questions (FAQ)
What is the difference between simple and compound interest?
Simple interest is calculated only on the original principal amount. Compound interest is calculated on the principal *plus* any interest that has already accumulated. This “interest on interest” effect means compound interest grows much faster over time.
How does compounding frequency (e.g., monthly) affect the result?
This calculator assumes annual compounding (once per year). More frequent compounding (e.g., monthly or daily) will result in a higher future value because the interest starts earning interest sooner. The formula becomes A = P(1 + r/n)^(nt), where ‘n’ is the number of compounding periods per year.
What is the “Rule of 72”?
The Rule of 72 is a quick mental shortcut to estimate how long it will take for an investment to double. You simply divide 72 by the annual interest rate. For example, at an 8% annual return, it will take approximately 9 years (72 / 8) for your money to double.
Can this calculator solve for the interest rate I need?
Yes. If you know your starting amount (Principal), your financial goal (Future Value), and how long you have (Term), this calculator can solve for the Annual Rate (R) you would need to achieve that goal.