Learn›Arithmetic ReasoningAR›Simple interest
Simple interest
Savings accounts, car loans, borrowed money: every interest question on the test uses the same one-line formula. The points are lost in the reading: interest or total? Months or years? Here is how to get both right.
Interest is rent paid on money
I = P × r × t
When you borrow money, you pay extra for using it; when you save, the bank pays you. That extra is the interest. With simple interest it is always taken from the original amount, the principal, so it is the same every year.
Interest or total?
The formula gives the interest only. If the question asks how much someone will have or will owe, add the principal back: total = P + I.
How to solve them
-
1
One formula: I = P × r × t
Write the rate as a decimal (5% = 0.05) and the time in years. Then multiply the three numbers. Multiplying principal by rate first gives you one year of interest, which is easy to check.
Next step: Interest or total?Example$800 saved at 5% simple interest for 3 years. How much interest?
- 5% = 0.05, so I = 800 × 0.05 × 3.
- One year: 800 × 0.05 = 40 dollars.
- Three years: 40 × 3 = 120.
Answer $120
-
2
Interest or total balance? Read the last line
“How much interest” wants I. “How much will she have”, “what is the balance” or “how much does he owe” want the total: the principal plus the interest.
total = P + I
Next step: Months to yearsAsks for the interestHow much interest does $800 earn in 3 years at 5%?
$120
Asks for the totalHow much is in the account after those 3 years?
800 + 120 = $920
-
3
Time must be in years: divide months by 12
The rate is per year, so a time given in months has to become a fraction of a year. These four come up again and again:
3 months3 ÷ 120.25 year6 months6 ÷ 120.5 year9 months9 ÷ 120.75 year18 months18 ÷ 121.5 yearsNext step: Find r, t or PExample$1,800 borrowed at 8% for 9 months. How much interest?
- 9 months = 9 ÷ 12 = 0.75 year.
- One year: 1,800 × 0.08 = 144 dollars.
- Three quarters of a year: 144 × 0.75 = 108.
Answer $108
-
4
Working backwards: find the rate, the time or the principal
If the question gives you the interest and asks for one of the other letters, divide the interest by the two letters you know.
r = I ÷ (P × t)
Next step: In your headFind the rate$600 earns $72 in 2 years
72 ÷ (600 × 2) = 0.06 = 6%
Find the time$900 at 4% earns $108
108 ÷ (900 × 0.04) = 3 years
Find the principal5% for 2 years earns $70
70 ÷ (0.05 × 2) = $700
-
5
Do it in your head with 1% and 10%
Interest is a percent problem in disguise. Find one year with the 10% and 1% shortcuts from the percents topic, then multiply by the number of years.
Next step: Simple, not compoundExample$3,500 at 3% simple interest for 4 years
- 1% of 3,500 is 35, so 3% is 3 × 35 = 105 dollars a year.
- 105 × 4 = 420.
Answer $420
-
6
Simple interest never earns interest on interest
Simple interest is always taken from the original principal, so it grows by the same amount each year. Interest on interest (compound interest) is a different formula; when a question says “simple,” use only P.
ShortcutSame amount every year
$800 at 5% earns $40 in the first year, $40 in the second and $40 in the third. A choice bigger than P × r × t has been compounded, and it is wrong for a simple-interest question.
4 traps in the answer choices
The test writes its wrong answers on purpose: each one is what you get if you make one of these mistakes.
The interest when the total is asked
$1,000 at 6% for 2 years. “How much will she have?”
Wrong$120
Right1,000 + 120 = $1,120
Months used as years
$4,000 at 3% for 6 months:
Wrong4,000 × 0.03 × 6 = $720
Right4,000 × 0.03 × 0.5 = $60
The percent not written as a decimal
$500 at 4% for 1 year:
Wrong500 × 4 = $2,000
Right500 × 0.04 = $20
Interest on interest
$800 at 5% simple interest, second year:
Wrong840 × 0.05 = $42 more
Right800 × 0.05 = $40 more
5 questions at test level
Pick an answer, then read why. No timer, no account.
$2,500 is deposited at 4% simple interest for 3 years. How much interest does it earn?
Show the answer
B. I = 2,500 × 0.04 × 3. One year is 100 dollars, so three years is 300. $100 is one year, $2,800 is the total balance, and $30,000 forgets to turn 4% into 0.04. The interest is $300.
Marcus borrows $1,200 at 7% simple interest for 2 years. How much does he owe at the end, interest included?
Show the answer
D. Interest: 1,200 × 0.07 = 84 a year, and 84 × 2 = 168. He owes the loan plus the interest: 1,200 + 168 = 1,368. $168 is only the interest and $1,284 counts one year. He owes $1,368.
How much simple interest does $3,000 earn at 5% in 8 months?
Show the answer
A. 8 months is 8/12 = 2/3 of a year. One year of interest is 3,000 × 0.05 = 150, and 2/3 of 150 is 100. $120 reads 8 months as 0.8 years, and $1,200 uses 8 years. The interest is $100.
A deposit of $750 earns $90 in simple interest over 3 years. What is the yearly interest rate?
Show the answer
B. r = I ÷ (P × t) = 90 ÷ (750 × 3) = 90 ÷ 2,250 = 0.04. 12% is 90 ÷ 750, which is three years of interest, not one. The rate is 4%.
A $5,000 loan charges 6% simple interest per year. After how many years will the interest reach $1,500?
Show the answer
C. t = I ÷ (P × r). One year of interest is 5,000 × 0.06 = 300 dollars, and 1,500 ÷ 300 = 5. 25 divides by 60 instead of 300. It takes 5 years.
9 flashcards
Tap a card to flip it. Keep the ones you miss until they stick.
All 9 cards known.
You finished simple interest.
Practice score: not taken yet Take the practice
Next topic: Distance, rate & timeSee this topic move.
In the course, every topic is drawn step by step on a whiteboard while a voice explains it, with timed practice tests and a plan for your test date. The first lessons of every module are free.
