Simple Interest — Definition, Formula & Examples

Simple Interest

A method of computing interest. Interest is computed from the (original) principal alone no matter how much money has accrued so far.

Formula: A = P(1 + nr)

     A = final amount
     P = principal, or original amount
     n = number of years
     r = rate of interest per year

Example:
$2,000 is deposited in an account paying 12% per year. Find the balance after 7 years using simple interest.

Solution:
P = $2,000, r = 0.12, and n = 7
A = $2,000(1 + 7·0.12) = $3,680

Key Formula

A = P(1 + nr)

Where:

$A$ = Final amount (principal plus all interest earned)
$P$ = Principal — the original amount deposited or borrowed
$n$ = Number of years the money is invested or borrowed
$r$ = Annual interest rate expressed as a decimal (e.g., 5% = 0.05)

Worked Example

Problem: You deposit $5,000 in a savings account that pays 6% simple interest per year. What is the balance after 4 years?

Step 1: Identify the values: principal P = $5,000, annual rate r = 0.06, and time n = 4 years.

P = 5000, \quad r = 0.06, \quad n = 4

Step 2: Substitute into the simple interest formula.

A = 5000(1 + 4 \cdot 0.06)

Step 3: Compute the product inside the parentheses.

4 \cdot 0.06 = 0.24

Step 4: Add 1 and multiply by the principal.

A = 5000(1.24) = 6200

Answer: The balance after 4 years is

6,200. The account earned

1,200 in total interest.

Another Example

This example solves for the unknown time n instead of the final amount A, showing how to rearrange the simple interest formula.

Problem: You borrow

3,000 at 8% simple interest per year. After some time, you owe a total of

3,720. How many years has the loan been outstanding?

Step 1: Write down what you know: P =

3,000, r = 0.08, A =

3,720. The unknown is n.

3720 = 3000(1 + n \cdot 0.08)

Step 2: Divide both sides by the principal to isolate the parenthetical expression.

\frac{3720}{3000} = 1 + 0.08n \quad \Rightarrow \quad 1.24 = 1 + 0.08n

Step 3: Subtract 1 from both sides.

0.24 = 0.08n

Step 4: Divide both sides by 0.08 to solve for n.

n = \frac{0.24}{0.08} = 3

Answer: The loan has been outstanding for 3 years.

Frequently Asked Questions

What is the difference between simple interest and compound interest?

Simple interest is calculated only on the original principal, so the interest earned each year stays the same. Compound interest is calculated on the principal plus all previously earned interest, so the amount grows faster over time. For example,

1,000 at 10% simple interest earns

100 every year, while at 10% compound interest the earnings increase each year because you earn interest on your interest.

How do you calculate simple interest for months instead of years?

Convert the number of months into a fraction of a year by dividing by 12. For instance, 9 months equals 9/12 = 0.75 years. Then use n = 0.75 in the formula. Alternatively, you can think of the interest earned as I = P · r · n, where n is the time in years expressed as a decimal.

When is simple interest used in real life?

Simple interest appears in short-term loans, car loans, some government bonds, and discount calculations. Banks and credit cards more commonly use compound interest, but simple interest is standard for many personal loans and is often used in introductory finance courses to build understanding before moving to compound interest.

Simple Interest vs. Compound Interest

	Simple Interest	Compound Interest
How interest is calculated	On the original principal only	On the principal plus all accumulated interest
Formula	A = P(1 + nr)	A = P(1 + r/k)^(kn), where k = compounding periods per year
Growth pattern	Linear — the same dollar amount of interest each period	Exponential — interest grows faster over time
Total amount earned	Less, for the same rate and time	More, because interest earns its own interest
Common uses	Short-term loans, car loans, some bonds	Savings accounts, mortgages, credit cards

Why It Matters

Simple interest is one of the first formulas you encounter in algebra and financial literacy courses. Understanding it is essential because it forms the foundation for compound interest, annuities, and other financial concepts you will study later. It also appears on standardized tests and in everyday situations like calculating the cost of a short-term loan or understanding a bond's return.

Common Mistakes

Mistake: Using the interest rate as a percentage instead of a decimal in the formula.

Correction: Always convert the percentage to a decimal before substituting. For example, 8% must be entered as r = 0.08, not r = 8. Using 8 would give a wildly inflated answer.

Mistake: Confusing the interest earned (I) with the total final amount (A).

Correction: The interest alone is I = Pnr. The final amount is A = P + I = P(1 + nr). If a problem asks "how much interest was earned," report I, not A. If it asks for the balance or total amount, report A.

Related Terms

Compound Interest — Interest computed on principal plus accumulated interest
Continuously Compounded Interest — Compound interest with infinitely many compounding periods
Principal — The original amount on which interest is calculated
Interest — The fee paid for borrowing or earning on money
Compute — To calculate or determine a numerical result
Linear Growth — Simple interest produces linear growth over time
Rate — The percentage at which interest accrues per period