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Principle — Definition, Formula & Examples

Principal

In finance, the original amount of money invested, deposited, or loaned.

 

 

See also

Interest, simple interest, compound interest, continuously compounded interest

Key Formula

I=P⋅r⋅tI = P \cdot r \cdot t
Where:
  • PP = Principal — the original amount of money
  • rr = Annual interest rate (as a decimal)
  • tt = Time in years
  • II = Interest earned or owed

Worked Example

Problem: You borrow $5,000 from a bank at a simple interest rate of 6% per year for 3 years. How much interest do you owe, and what is the total amount you repay?
Identify the principal: The principal is the original amount borrowed.
P=5,000P = 5{,}000
Calculate the interest: Use the simple interest formula with r = 0.06 and t = 3.
I=5,000×0.06×3=900I = 5{,}000 \times 0.06 \times 3 = 900
Find the total repayment: Add the interest to the principal to find the total amount owed.
A=P+I=5,000+900=5,900A = P + I = 5{,}000 + 900 = 5{,}900
Answer: The interest owed is 900,andthetotalrepaymentis900, and the total repayment is5,900. The principal remains $5,000 throughout — it is simply the starting amount on which the interest was calculated.

Another Example

Problem: You invest $2,000 in a savings account that earns 5% compound interest per year. After 2 years, how much of your balance is principal and how much is earned interest?
Identify the principal: The principal is your original deposit.
P=2,000P = 2{,}000
Calculate the balance after 2 years: Use the compound interest formula.
A=2,000×(1+0.05)2=2,000×1.1025=2,205A = 2{,}000 \times (1 + 0.05)^2 = 2{,}000 \times 1.1025 = 2{,}205
Separate principal from interest: Subtract the principal from the total to find the interest earned.
Interest=2,205−2,000=205\text{Interest} = 2{,}205 - 2{,}000 = 205
Answer: After 2 years your balance is 2,205.Ofthat,2,205. Of that,2,000 is your original principal and $205 is earned interest. Notice the principal itself did not change — only the interest grew on top of it.

Frequently Asked Questions

What is the difference between principal and interest?
Principal is the original amount of money you start with — the amount you invest, deposit, or borrow. Interest is the additional money earned on (or owed on) that principal over time. When you repay a loan, part of each payment goes toward reducing the principal and part covers the interest.
Does the principal change over time?
In simple interest, the principal stays constant. In compound interest, the principal itself does not change, but interest is calculated on the growing total (principal plus previously earned interest). In loan repayment, the outstanding principal decreases as you make payments toward it.

Principal vs. Interest

Principal is the original sum of money — the starting point. Interest is the cost of borrowing that money (for a loan) or the reward for lending/investing it. Every interest calculation begins with the principal. Without a principal, there is no interest. For example, if you deposit 1,000andearn1,000 and earn50 in interest, the 1,000istheprincipalandthe1,000 is the principal and the50 is the interest.

Why It Matters

Every financial calculation involving loans, savings, or investments starts with the principal. Knowing your principal lets you determine how much interest you will earn or owe. Whether you are comparing mortgage offers, evaluating savings accounts, or planning investments, understanding the principal is the first step to making informed financial decisions.

Common Mistakes

Mistake: Confusing "principal" with "principle."
Correction: "Principal" (with an 'a') refers to the original amount of money or a person in authority. "Principle" (with an 'e') means a fundamental rule or belief. In math and finance, you always mean principal.
Mistake: Thinking the principal grows in a simple interest calculation.
Correction: With simple interest, the principal stays the same for the entire duration. Interest is always calculated on the original principal, not on any accumulated total. It is only with compound interest that the base for calculation grows over time.

Related Terms