How to Calculate Simple Interest: Step by Step

What simple interest is

Simple interest is the interest on a sum of money, worked out once on the principal and paid the same every year — it never compounds. The total amount is the principal plus the interest, and the schedule shows the balance growing one identical year at a time. On the defaults here — $10,000.00 at 5% for 3 years — the interest is $1,500.00 and the total is $11,500.00. Every figure here is checked against the simple interest + principal calculator.

The simple interest formula

Interest = principal × annual rate × time in years. Total amount = principal + interest. The rate is a decimal in the formula — 5% is 0.05 — and the time is in years, so six months is 0.5 of a year and three months is 0.25. The schedule shows each year separately: year interest = principal × rate × the fraction of that year, and the running balance after each year.

Step 1: Write down the principal, the rate, and the time

Write down the three numbers the formula needs. The principal is the starting sum — $10,000.00 on the defaults. The annual rate is the rate per year as a percent — 5% on the defaults. The time is how long the money is held, in years — 3 years on the defaults. If the time is in months, divide by 12 first.

Step 2: Multiply the principal by the rate and the time

Multiply the principal by the rate and the time for the interest. On the defaults that is $10,000.00 × 5% × 3 = $1,500.00 of interest. The rate is 0.05 as a decimal, so the multiplication is $10,000.00 × 0.05 × 3 = $1,500.00. The interest is the same every year — $500.00 a year — because simple interest never compounds.

Step 3: Add the interest to the principal for the total

Add the interest to the principal for the total amount. On the defaults that is $10,000.00 + $1,500.00 = $11,500.00. The total is what you get back at the end of the term: the money you started with, plus everything it earned. A $25,000.00 principal at the same rate and time earns $3,750.00 of interest, for a total of $28,750.00 — two and a half times the principal, two and a half times the interest.

Step 4: Lay out the year-by-year schedule

Lay out the year-by-year schedule, so you can see the balance grow. On the defaults the schedule is three identical years: year 1 interest is $500.00 and the balance is $10,500.00; year 2 interest is $500.00 and the balance is $11,000.00; year 3 interest is $500.00 and the balance is $11,500.00. A final partial year earns interest only for its fraction of the year: six months is 0.5 of a year, so the interest is $250.00 and the total is $10,250.00, on a single partial-year row.

Step 5: Reverse it when you need a target

Reverse it when you need a target. To earn $2,000 of interest on $10,000.00 over 3 years, the rate must be 6.67% — the exact rate is 6.6667%, and at the displayed 6.67% the interest is $2,001.00, $1 over the target, because the rate is rounded. To end with a $15,000 total at 5% for 3 years, the principal must be $13,043.48: at $13,043.48 the total is $15,000.00 exactly. And the first whole number of years at which the interest reaches $2,000 is 4 years: at 4 years the interest is $2,000.00, while 3 years gives $1,500.00 and 5 years gives $2,500.00.

Step 6: Watch the traps

Watch the traps. First, simple interest never compounds — the interest is the same every year, while most real loans compound or amortize, so the interest changes over the term and this formula does not model that. Second, the rate is annual: a monthly rate of 0.5% is 6% a year, not 0.5% a year, and the time must be in years to match. Third, a partial year earns only its fraction — three months at 5% is $125.00 on $10,000.00, not $500.00. And fourth, ten years at 5% earns $5,000.00 of interest on $10,000.00 — half the principal again.

Worked example

Put the six steps together for $10,000.00 at 5% for 3 years. The interest is $10,000.00 × 5% × 3 = $1,500.00. The total amount is $10,000.00 + $1,500.00 = $11,500.00. The schedule is $500.00 of interest a year: $10,500.00 after year 1, $11,000.00 after year 2, and $11,500.00 after year 3. A $25,000.00 principal at the same rate and time earns $3,750.00 for a total of $28,750.00, and ten years at 5% earns $5,000.00 of interest for a total of $15,000.00.

How the numbers change

A rate of 8% lifts the interest to $2,400.00 and the total to $12,400.00. A principal of $5,000.00 at 3% for 5 years earns $750.00 for a total of $5,750.00. A principal of $100,000.00 at 6% for 1 year earns $6,000.00 for a total of $106,000.00. A principal of $50,000.00 at 4% for 7 years earns $14,000.00 for a total of $64,000.00.

Working backwards

It also runs in reverse. To earn $1,250.00 of interest takes 2.50 years at 5% on $10,000.00: 2.49 years gives $1,245.00 and 2.51 gives $1,255.00. To end with a $20,000 total takes a rate of 33.33%: at 33.33% the total is $19,999.00, $1 under the target, because the exact rate is 33.3333% and 33.34% gives $20,002.00. To earn $3,000 of interest takes a principal of $20,000.00: at $20,000.00 the interest is $3,000.00 exactly.

What the calculation leaves out

Four things are left out. First, this is simple interest only — it never compounds, while most real loans compound or amortize and the interest changes over the term. Second, it does not model fees, late charges, or taxes on the interest. Third, it does not model a rate that changes part-way through. Fourth, it does not model monthly or daily compounding. For the interest alone, without the total, see the simple interest calculator, and for what a sum grows to with compounding, see the future value calculator.

What to do next

Run your own numbers through the simple interest + principal calculator — and if the term is in months, divide by 12 before you multiply, so the rate and the time are both annual.