Money
Simple Interest Formula
The simple interest formula is I = Prt: interest equals the principal times the annual rate (as a decimal) times the time in years. $12,000 at 7% for 5 years earns 12,000 × 0.07 × 5 = $4,200. This guide shows how to calculate simple interest step by step, how to get the total amount, how to rearrange the formula for any unknown, how to handle months and days, and how to solve the word problems that wrap it in a story.
What is the simple interest formula?
Each letter has one job:
- P, the principal, is the starting amount: what you borrow, or what you deposit.
- r, the rate, is the share of the principal charged or paid per year. A rate of 7% is written as 0.07.
- t, the time, is how many years the money is out. Half a year is 0.5.
- I, the interest, is the extra money on top of the principal. It is not the total.
The formula is often written without multiplication signs as I = Prt, which is the same thing: letters written side by side are multiplied. If you just want an answer, the simple interest calculator runs the formula for you and solves for any of the four values.
Why the formula works
A rate of 7% a year means that for every $1 of principal, 7 cents of interest is added each year. So one year of interest on $12,000 is 12,000 × 0.07 = $840. Simple interest never changes the base it is charged on, so every year adds the same $840. Five years is five lots of $840:
Multiplying by t is a shortcut for adding the same yearly interest t times. That is the whole idea: one year of interest is P × r, and you need t of them. Because the formula is just a percentage of a number scaled up by time, the percentage formula is doing most of the work inside it.
How to calculate simple interest, step by step
- Write down the principal. Use the amount borrowed or deposited, not any later balance.
- Turn the rate into a decimal. Divide the percentage by 100: 3.5% becomes 0.035. The percent to decimal calculator does this for any rate.
- Put the time in years. Months ÷ 12, days ÷ 365. Leave it as a fraction if it does not divide evenly.
- Multiply the three together. The result is the interest.
- Add the principal if you need the total. Total amount
A = P + I.
Example: $800 at 3.5% for 2 years
A small deposit with a whole number of years.
The deposit earns $56 and is worth $856 at the end of the two years.
Example: $12,000 at 7% for 5 years
A larger loan over a longer term.
The borrower repays $16,200, of which $4,200 is interest. Multiplying the principal by the rate first gives the yearly interest, which makes the answer easy to sense-check.
The total amount formula: A = P(1 + rt)
When the question asks how much will be repaid or how much the account will hold, you want the total amount, not just the interest. Start from A = P + I and substitute I = Prt:
Factoring out P is the distributive property run backward, and it gives a useful one-step multiplier. For 7% over 5 years, 1 + 0.07 × 5 = 1.35, so every dollar becomes $1.35: 12,000 × 1.35 = 16,200.
The multiplier also lets you work backward from a total to the principal. If a loan at 7% for 5 years ends with $16,200 owed, the principal was:
This is the same idea as undoing a percentage increase, which the reverse percentage calculator does for a single change. Do not subtract 35% of $16,200; that gives $10,530, the wrong answer, because the 35% was a percentage of $12,000, not of $16,200.
Rearranging I = Prt for principal, rate or time
The formula has four quantities. Know any three and you can find the fourth by dividing the interest by the two known factors.
| Unknown | Formula | Example | Answer |
|---|---|---|---|
| Interest | I = Prt | P = $6,000, r = 7%, t = 3 | $1,260 |
| Principal | P = I ÷ (rt) | I = $1,530, r = 4.25%, t = 2 | $18,000 |
| Rate | r = I ÷ (Pt) | I = $1,260, P = $6,000, t = 3 | 0.07 = 7% |
| Time | t = I ÷ (Pr) | I = $900, P = $5,000, r = 4.5% | 4 years |
Example: finding the rate
A $6,000 loan costs $1,260 in interest over 3 years.
Remember to convert the decimal back into a percentage at the end. The decimal to percent calculator does that step if the decimal is awkward.
Example: finding the principal
How much must be invested at 4.25% to earn $1,530 in 2 years?
An $18,000 deposit does it. Check: 18,000 × 0.0425 × 2 = 1,530.
Example: finding the time
How long does $5,000 at 4.5% take to earn $900?
Each year earns $225, and four of those make $900. If the answer comes out as a decimal such as 2.75 years, multiply the decimal part by 12 to read it as months: 0.75 × 12 = 9, so 2 years 9 months.
Every rearrangement is the same move: divide both sides by the factors you know. This is the multiplication–division relationship that proportions rely on too.
Simple interest with months and days
An annual rate needs time in years. Convert first, then use the formula as normal.
Example: $2,500 at 12% for 4 months
Months are twelfths of a year.
The interest is $100. Keeping t as the fraction 4/12 avoids rounding 0.3333…
Example: $7,500 at 3.9% for 30 months
More than a year is fine; t is simply greater than 1.
The interest is $731.25 and the total is $8,231.25.
Example: $3,000 at 4.5% for 200 days
Days are counted against a 365-day year here.
The interest is about $73.97. Do the division by 365 last and round only the final answer, using the rounding to decimal places guide if you need a rule for the cents.
Simple interest on $1,000: a reference table
Simple interest scales in proportion, so this table works for any principal: for $5,000, multiply every entry by 5; for $250, divide by 4.
| Rate | 1 year | 3 years | 5 years | 10 years |
|---|---|---|---|---|
| 2% | $20 | $60 | $100 | $200 |
| 3% | $30 | $90 | $150 | $300 |
| 4% | $40 | $120 | $200 | $400 |
| 5% | $50 | $150 | $250 | $500 |
| 6% | $60 | $180 | $300 | $600 |
| 8% | $80 | $240 | $400 | $800 |
| 10% | $100 | $300 | $500 | $1,000 |
Reading across a row shows the defining feature of simple interest: double the time and you double the interest. That is not true of compound interest.
Simple interest word problems, solved
Homework and test questions wrap the same formula in a short story. The arithmetic is never the hard part; the hard part is pulling the right three numbers out of the sentence and noticing whether the question wants the interest or the total. Before you calculate anything, answer four questions:
- What is the principal? The amount deposited, borrowed or invested at the start. Ignore any later balance.
- What is the yearly rate? Change it to a decimal. If the problem gives a monthly rate, multiply by 12 first.
- How long, in years? Months ÷ 12, days ÷ 365. A phrase like “keeps the money in the account” with no deposits or withdrawals is just telling you the principal does not change.
- Interest or total? “How much interest” or “how much will she earn” wants
I. “How much will she have”, “how much in all”, “total repaid” or “worth at the end” wantsA = P + I.
Problem 1: interest earned on a deposit
Maya deposits $4,200 in a savings account that pays 3.2% simple interest. She makes no other deposits or withdrawals. How much interest will she receive after 4 years?
She receives $537.60 in interest. The question asks for interest, so the principal is not added. If it had asked how much is in the account, the answer would be $4,737.60.
Problem 2: total repaid on a loan in months
Carlos borrows $1,850 at 9% simple interest for 18 months. How much does he repay in total?
He repays $2,099.75. Plugging in 18 for t would give $2,997 of interest, twelve times too much, which is the most common wrong answer to this kind of problem.
Problem 3: finding the interest rate
A $2,400 deposit earns $162 in simple interest over 3 years. What annual interest rate does the account pay?
The rate is 2.25% a year. A quick check: one year of interest is $54, and three of those make $162.
Problem 4: how long until a balance is reached
How long will it take $6,000 invested at 4% simple interest to grow to $7,080?
It takes 4.5 years, or 4 years and 6 months. The problem gives a target total, so the interest has to be worked out first by subtracting the principal.
Problem 5: finding the original deposit from the total
After 5 years at 6% simple interest, an account holds $3,380. How much was deposited?
The deposit was $2,600. Check: 2,600 × 0.06 × 5 = 780, and 2,600 + 780 = 3,380. Taking 30% off $3,380 would give $2,366, which is wrong for the reason explained in the total amount section above.
Problem 6: rounding to the nearest cent
Priya borrows $900 at 6.5% simple interest for 9 months. How much interest does she owe, to the nearest cent?
She owes $43.88. Keep every digit until the last step and round once; rounding 9 ÷ 12 to 0.8 early would give $46.80 instead.
Problem 7: simple or compound, which pays more?
You have $5,000 for 3 years. Bank A pays 4% simple interest. Bank B pays 3.9% compounded once a year. Which earns more?
Bank B earns about $8 more, even with the lower rate, because each year’s interest starts earning interest of its own. Over longer terms the gap grows quickly, as the next section shows.
To check any of these, enter the principal, rate and time in the simple interest calculator; set it to solve for rate or time for problems 3 and 4.
How simple interest differs from compound interest
Simple interest is always charged on the original principal. Compound interest is charged on the principal plus any interest already added, so the base keeps growing:
The first is linear in t; the second is an exponent, which the exponent rules guide covers. One consequence: at 5% simple interest, money doubles when rt = 1, which takes 1 ÷ 0.05 = 20 years. At 5% compounded yearly it doubles in about 14.21 years. For short terms of a year or less, the two give the same or nearly the same answer, which is why short loans are often quoted with simple interest.
Common mistakes
- Using the percentage instead of the decimal.
800 × 3.5 × 2 = 5,600is 100 times too big. Use 0.035. - Leaving time in months. With an annual rate,
t = 30instead of 2.5 makes the interest 12 times too large. - Confusing interest with the total.
Iis the extra amount. The total isP + I. - Reversing a total by subtracting a percentage of it. To get
PfromA, divide by(1 + rt); do not takertoffA. - Forgetting to turn the rate back into a percent.
r = 0.07is 7%, not 0.07%. - Treating a monthly rate as annual. 1.5% a month is 18% a year. Convert it before using an annual time.
Frequently asked questions
What is the formula for simple interest?
The simple interest formula is I = Prt, where P is the principal, r is the annual rate as a decimal and t is the time in years. The total amount at the end is A = P(1 + rt). For $800 at 3.5% over 2 years, I = 800 × 0.035 × 2 = $56.
How do you calculate simple interest?
Convert the rate to a decimal, put the time in years, and multiply principal by rate by time. For $12,000 at 7% for 5 years: 12,000 × 0.07 × 5 = $4,200. Add the principal to get the total of $16,200. Converting months or days to years before multiplying is the step people most often skip.
How do you solve a simple interest word problem?
Find the principal, the yearly rate as a decimal and the time in years, then decide whether the question asks for the interest or the total. Multiply P × r × t for the interest and add P only if the question wants the final amount. For $4,200 at 3.2% for 4 years, the interest is 4,200 × 0.032 × 4 = $537.60.
What is the simple interest on $1,000 at 5% for 3 years?
It is $150. One year at 5% is 1,000 × 0.05 = $50, and three years is three times that. The total amount at the end of the term is $1,150. Because simple interest is proportional, $2,000 on the same terms would earn exactly double, $300.
How do you find the principal in simple interest?
Divide the interest by the rate times the time: P = I ÷ (rt). To earn $1,530 at 4.25% over 2 years, P = 1,530 ÷ 0.085 = $18,000. If you know the total amount instead of the interest, use P = A ÷ (1 + rt).
How do you find the time in simple interest?
Divide the interest by the principal times the rate: t = I ÷ (Pr). For $900 of interest on $5,000 at 4.5%, t = 900 ÷ 225 = 4 years. A decimal answer such as 2.75 years means 2 years and 9 months, since 0.75 × 12 = 9.
What does r stand for in I = Prt?
r is the interest rate per year, written as a decimal. A rate of 7% becomes 0.07 and a rate of 4.25% becomes 0.0425. If a rate is quoted per month, multiply it by 12 to get the annual rate before using it with time measured in years.
Why is it called simple interest?
Because the interest is always worked out on the original principal and never added back to it, so every year earns the same amount. That makes the arithmetic a single multiplication. Compound interest adds each period’s interest to the balance, so later interest is charged on earlier interest and the formula needs an exponent.
Calculators for this
Every one of these shows the working, so you can check the method as well as the answer.
More guides
https://fourfunctioncalculator.com/simple-interest-formula/