Simple Interest
Simple Interest
Interest earned on the original principal only, with no interest on interest: principal times rate times time. Used for short-term loans, some bonds' accrued interest, and as the baseline that compound interest is measured against.
When to use: Use for instruments that quote simple interest (treasury bills, many short-term notes, late-payment charges) and to see how much compounding adds over the same period.
Formula
Variables
| Symbol | Name | Description | Unit |
|---|---|---|---|
| SimpleInterest | Simple Interest | Total interest earned over n years | $ |
| PV | Present Value | The current worth of a future sum | $ |
| k | Interest Rate | Nominal annual interest rate as a decimal | % |
| n | Number of Years | Investment time horizon in years | years |
Real-Life Examples
Example 1: Three-Year Note
A $10,000 note pays 5% simple interest for 3 years.
Given
Step-by-Step
Simple interest yields exactly $500 a year. The same note compounded annually would earn $1,576.25, so compounding adds $76.25 over three years.
Example 2: Six-Month Loan
A $2,500 loan at 8% simple interest for six months.
Given
Step-by-Step
Half a year at 8% is 4% of the principal. Over short periods simple and compound interest are nearly identical.
Frequently Asked Questions
Over long periods and at high rates. For a few months the two are close; over decades, compounding produces several times the simple-interest amount.
Yes. Simple interest is proportional to time, so half a year earns exactly half a year's interest.