How to use the four calculator modes
Pick the one value you want to find: the end balance, the principal, the time or the rate. The calculator hides that field and asks for the other three, so you can never type in a number that is silently ignored. Enter the amounts, choose whether the rate and the time are monthly or yearly, and press Calculate. The page shows the answer, the calculation steps with the correct label for each step, a straight-line chart and a schedule you can export.
The starting example is 20,000 at 3% a year for 10 years, which earns 6,000 of interest and ends at 26,000. Edit any field and the old results disappear until you calculate again. Everything runs in your browser.
Simple interest formula: I = P × r × t
Simple interest is interest paid only on the original amount. The formula is I = P × r × t, where P is the principal, r is the rate as a decimal for one time unit and t is the number of those time units. Nothing is added back to the principal, so each period earns the same interest. Because the growth is linear, doubling the time doubles the interest, and doubling the rate does the same.
Principal, interest and final balance
The end balance is the principal plus the interest, A = P + I = P × (1 + r × t). With 20,000 at 3% for 10 years, the interest is 20,000 × 0.03 × 10 = 6,000 and the balance is 26,000. Because the growth is linear, the balance rises by the same 600 every year, which is why the chart on this page is a straight line and the schedule shows equal steps.
Match monthly and annual units
The most common mistake is mixing units, such as a yearly rate with a time in months. The rate and the time must use the same period. A rate of 0.5% a month for 6 months is 0.005 × 6 = 3% of the principal, so 10,000 earns 300 and ends at 10,300. The same loan as a yearly rate is 6% a year, which is 0.5% × 12, for 0.5 years: 10,000 × 0.06 × 0.5 = 300, the same 10,300.
This page converts for you. When you switch a unit, the number you typed is converted so the rate or time stays the same, instead of silently meaning something else. A monthly rate is multiplied by 12 to get the simple yearly equivalent, and a time of 18 months becomes 1.5 years. That is not the same as compounding a monthly rate into an APY, which would add interest on interest and belongs on a compounding calculator.
Solve for principal, time or rate
Each inverse comes from rearranging A = P × (1 + r × t). To find the principal, divide the end balance by the growth factor: P = A ÷ (1 + r × t). For an end balance of 30,000 at 3% for 10 years, P = 30,000 ÷ 1.3 = 23,076.92. To find the time, use t = (A ÷ P − 1) ÷ r. With 20,000 growing to 30,000 at 3%, t = (1.5 − 1) ÷ 0.03 = 16.6667 years. To find the rate, use r = (A ÷ P − 1) ÷ t, so 20,000 becoming 30,000 in 10 years needs 0.5 ÷ 10 = 5% a year.
Some inputs cannot identify the answer. If the principal and the end balance are equal and the rate is zero, any time fits, so the time is indeterminate. If the end balance differs from the principal while the rate or the time is zero, nothing fits and there is no solution. A balance below the principal would need a negative rate or time, which this calculator does not support. The page names these cases and never invents a number.
Each solve also works as a check on the others. Start from the first example's balance of 26,000 and solve for the principal at 3% for 10 years: 26,000 ÷ 1.3 = 20,000, the original amount. Solving for the time from 20,000 to 26,000 at 3% gives 10 years, and solving for the rate gives 3% a year. If the four answers disagree with each other, one of the units is mismatched.
Read the linear interest schedule
The schedule lists the principal, the interest earned so far and the balance after each full year, or each full month when you chose months, and adds an exact final row when the term ends partway through a period. These rows are elapsed periods from the start, not legal due dates, and they are not repayments. The CSV export contains every row with fixed column headings.
For the 10-year example the table has 11 rows, one for each year from 0 to 10, and the last row equals the end balance of 26,000. When the term is not a whole number of periods, for example 2.5 years, the final row is the exact endpoint after the last full year. A long monthly term can run to 12,001 rows, so the page shows the first rows and lets you open the rest, while the CSV always contains all of them.
Simple interest versus compound interest
Compound interest adds each period's interest to the balance, so later periods earn interest on earlier interest. The two start together and then separate. For 10,000 at 5% a year, the balances are:
| Year | Simple balance | Compound balance |
|---|---|---|
| 1 | 10,500.00 | 10,500.00 |
| 2 | 11,000.00 | 11,025.00 |
| 3 | 11,500.00 | 11,576.25 |
| 4 | 12,000.00 | 12,155.06 |
| 5 | 12,500.00 | 12,762.82 |
After five years the simple balance is 12,500 and the annual compound balance is 12,762.82. That is an illustration of a balance left alone, not of a repayment plan. The gap widens every year because compounding earns interest on interest while simple interest does not: after one year both balances are 10,500, and after five years the compound balance is 262.82 higher. Whether a real product uses simple or compound interest depends on its terms, so read the agreement before relying on either model, and remember that neither figure includes tax or fees. Real products differ in how they credit interest. To compare compound balance growth with your own figures, use the compound interest calculator.
Simple interest is not an amortizing loan payment
On most car loans and mortgages you repay principal along with interest, so the balance shrinks and the interest charged each month shrinks with it. Here the principal stays fixed for the whole period, so this model does not produce a monthly instalment. In everyday speech a simple interest loan sometimes means a loan whose interest is charged only on the outstanding balance, with each payment reducing principal. That is a different calculation from the one on this page, which holds the principal constant and has no payment schedule. If you need the payment on a loan that amortizes, calculate reducing-balance loan payments instead. If you are comparing quoted rates that compound differently, convert nominal and effective rates first.
Simple interest questions
How do I calculate simple interest?
Multiply the original principal by the rate as a decimal and by the time in matching units. Add the principal to get the balance. For 20,000 at 3% a year for 10 years, that is 20,000 × 0.03 × 10 = 6,000 of interest and a balance of 26,000.
Can I find the principal?
Yes. Divide the final balance by 1 plus the rate times the time. Use the same time unit for the rate and the time, and the answer is the starting amount that grows to your final balance.
Can I use months?
Yes. Match a monthly rate to a time in months, or convert both to yearly units. The page converts the number you typed when you change a unit, so 3% a year becomes 0.25% a month and 10 years becomes 120 months without changing the meaning.
Why can time or rate be indeterminate?
At a zero rate or zero time, equal starting and ending balances do not identify the missing variable, because every value fits. The page says so instead of choosing a value for you.
Is this my monthly loan payment?
No. This model leaves the principal unchanged. Use the reducing-balance payment tool for a loan that amortizes, because there the balance, and therefore the interest each month, falls as you repay.
Next steps
To keep going, compare compound balance growth, calculate reducing-balance loan payments or convert nominal and effective rates. Whichever tool you choose, keep the rate and the time in matching units and compare the answer with your original terms. Each tool uses the same units, so your numbers carry across.