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Level 7Grade 7skill: simple_interest· 8 min read

Simple Interest Explained

In short: Simple interest is a flat yearly fee on the original principal: SI = (P × R × T) ÷ 100, with T always in years. Divide by 100, convert months to years first, and remember the amount to repay is principal + interest, not the interest alone.

The one formula, and the two things people get wrong with it

Simple interest is a flat rental fee on money. You lend (or borrow) a principal, and each year it earns a fixed percentage of that original amount — never on anything that has piled up since. Three numbers go in: the principal P, the yearly rate R (a percent), and the time T in years. One number comes out: the interest.

The formula is SI = (P × R × T) ÷ 100. That little ÷ 100 is the whole point of the word "percent" — 8% means 8 per hundred, so you divide. Miss it and your answer is 100 times too big.

Two traps live inside this simple-looking formula, and grade-7 papers hunt for both. First: the question often asks for the amount to repay, not the interest — and Amount = Principal + Interest, so you are not finished when you find SI. Second: T is in years. If the problem says 8 months or 18 months, convert before you multiply, or every later step is wrong.

  1. Write down P, R, and T. If T is given in months, convert it to years by dividing by 12; if in days, divide by 365.
  2. Multiply P × R × T.
  3. Divide that product by 100. This is the simple interest, SI.
  4. Re-read the question. If it asks for the amount (total to repay, final balance), add the principal back: Amount = P + SI.
  5. If instead you are given the interest and asked for P, R, or T, put the known numbers into SI = PRT/100 and solve for the missing one.

Why simple interest never snowballs — and how to exploit that Why it works

Flat, not snowballing
Every year you earn the same interest, always on the original principal. Your money grows in a straight line, never compounding.

$8,000 at 7.5% earns $600 in year 1, $600 in year 2, and still exactly $600 in year 5. Five years = 5 × $600 = $3,000.

Two different questions
Interest is the extra you earn; amount is principal plus that interest. Decide which one the question wants before you commit to an answer.

Borrow $9,000 at 8% for 2 years → the interest is $1,440, but the amount to repay is $9,000 + $1,440 = $10,440.

Clock in years
You must put T in years: divide months by 12, days by 365. Convert first, then multiply — not the other way round.

6 months = 6/12 = 1/2 year, so at 8% on $15,000 the interest is 15000 × 8 × (1/2) ÷ 100 = $600, not $7,200.

Multiply, don't re-base
Find one year's interest once, then multiply by the number of years. You never recalculate on a grown balance — that would be compound interest.

One year on $5,000 at 12% is $600. Two years is simply 2 × $600 = $1,200 — not $600 + 12% of $5,600.

Here is the genuine insight that turns hard problems into fast ones: because the interest is flat, the whole formula is proportional in every direction. Double the time, double the interest. Half the principal, half the interest. So you rarely need to restart a calculation — find one clean piece (one year's interest, or the interest on $1,000) and scale it. And when a problem grows a balance year after year, that is your signal it is compound interest, not this.

Five worked examples, from clean to sneaky

Sophie deposits $12,000 at 9% per annum simple interest for 8 months. How much interest does she earn? = $720. (Using 8 instead of 8/12 gives $8,640 — the classic unit trap.)
  1. T is in months, so convert: 8 months = 8/12 = 2/3 year.
  2. SI = (P × R × T) ÷ 100 = (12000 × 9 × 2/3) ÷ 100.
  3. 12000 × 9 = 108,000; × 2/3 = 72,000.
  4. 72,000 ÷ 100 = 720.
Noah borrows $6,500 at 6% per annum for 3 years. What total amount must he repay? = $7,670 to repay. ($1,170 is only the interest — stopping there is the amount-vs-interest trap.)
  1. SI = (6500 × 6 × 3) ÷ 100.
  2. 6500 × 6 = 39,000; × 3 = 117,000.
  3. 117,000 ÷ 100 = 1,170. That is the interest, not the answer.
  4. The question asks for the amount: A = P + SI = 6500 + 1170 = 7,670.
An investment earns $450 in simple interest over 2 years at 5% per annum. What was the principal? = $4,500. Check: 4500 × 5 × 2 ÷ 100 = 450. ✓
  1. Start from SI = PRT/100 with SI = 450, R = 5, T = 2.
  2. 450 = (P × 5 × 2) ÷ 100 = (P × 10) ÷ 100 = P ÷ 10.
  3. So P = 450 × 10.
  4. P = 4,500.
Which earns more interest: Plan A — $10,000 at 8% for 3 years, or Plan B — $10,000 at 6% for 5 years? By how much? = Plan B earns $600 more. (A bigger rate over less time can still lose — you must compute both.)
  1. Plan A: 10000 × 8 × 3 ÷ 100 = 240,000 ÷ 100 = 2,400.
  2. Plan B: 10000 × 6 × 5 ÷ 100 = 300,000 ÷ 100 = 3,000.
  3. The higher rate is not automatically the winner — the extra two years tip it.
  4. Difference = 3,000 − 2,400 = 600, in Plan B's favour.
How long will $5,000 take to earn $2,000 in simple interest at 10% per annum? = 4 years. Check: 5000 × 10 × 4 ÷ 100 = 2,000. ✓
  1. Use SI = PRT/100 with SI = 2000, P = 5000, R = 10.
  2. 2000 = (5000 × 10 × T) ÷ 100 = (50000 × T) ÷ 100 = 500T.
  3. T = 2000 ÷ 500.
  4. T = 4.

Seven ways this goes wrong — and the exact fix

Forgetting to divide by 100

✗ $500 at 8% for 1 year → 500 × 8 × 1 = $4,000.

8% does not mean "multiply by 8" — it means 8 per hundred, i.e. 0.08. Treating the percent as a whole number inflates the answer 100-fold.

Fix: Always ÷ 100: SI = 500 × 8 × 1 ÷ 100 = $40.

percent_as_whole

Giving the interest when the amount was asked

✗ $6,500 borrowed at 6% for 3 years, "amount to repay" → $1,170.

$1,170 is a correct intermediate step — it is the interest — but the question wanted the total to hand back. You stopped one step early.

Fix: Add the principal: Amount = 6,500 + 1,170 = $7,670.

partial_computation

Dividing by the wrong power of ten

✗ $2,500 at 4% for 3 years → $30 (divided the 30,000 by 1,000 instead of 100).

The decimal point slid one place too far. 2500 × 4 × 3 = 30,000, and 30,000 ÷ 100 is 300, not 30.

Fix: Divide by exactly 100 for a percent: SI = $300.

decimal_point_shift

Adding the rate and time instead of multiplying

✗ $4,000 at 5% for 2 years → 4000 × (5 + 2) ÷ 100 = $280.

Rate and time are multiplied, not added. Adding them treats "5% for 2 years" as if it were a single 7% — which is not what the formula says.

Fix: Multiply through: 4000 × 5 × 2 ÷ 100 = $400.

wrong_operation

Using months as if they were years

✗ $12,000 at 9% for 8 months → 12000 × 9 × 8 ÷ 100 = $8,640.

T must be in years, but 8 was left as "8 months" and multiplied in directly — mixing months into a per-annum formula.

Fix: Convert first: 8 months = 8/12 year, so SI = 12000 × 9 × (8/12) ÷ 100 = $720.

unit_mismatch

Subtracting in the wrong order

✗ "How much more does Plan B ($3,000) earn than Plan A ($2,400)?" → 2,400 − 3,000 = −$600.

The comparison was set up backwards. A negative answer to "how much more" is a signal the two values were swapped.

Fix: Subtract the smaller from the larger: 3,000 − 2,400 = $600 more.

sign_error

Charging interest on the grown balance

✗ $8,000 at 10% for 2 years, simple interest → year 1: $800, then 10% of $8,800 = $880, total $1,680.

Simple interest is always taken on the original principal. Using the year-1 balance ($8,800) as the new base is compounding — the wrong base for this problem.

Fix: Keep the base fixed at $8,000: $800 + $800 = $1,600.

base_confusion

Practice: simple interest

Work these the careful way — convert time to years first, then decide whether the question wants the interest or the full amount before you lock in an answer.

Before and after this skill

First, make sure of

Frequently asked questions

What is the difference between simple and compound interest?

Simple interest is always calculated on the original principal, so it earns the same amount every year and grows in a straight line. Compound interest is recalculated on the growing balance, so it snowballs. If a problem re-bases the interest on last year's total, it is compound — not the simple-interest formula on this page.

Do I always divide by 100?

Yes, whenever the rate is written as a percent. "Percent" means "per hundred," so 6% is 6/100. The ÷ 100 in SI = (P × R × T) ÷ 100 is what turns the rate number into an actual fraction. Skipping it makes your answer exactly 100 times too large.

How do I handle a time given in months or days?

Convert it to years first, because the rate is "per annum." Divide months by 12 (9 months = 9/12 = 3/4 year) or days by 365. Do the conversion before you multiply — plugging in "9" for 9 months is one of the most common ways to get a wildly wrong answer.

Is the "amount" the same as the "interest"?

No, and papers exploit this. The interest is the extra money earned or owed; the amount is the principal plus that interest (Amount = P + SI). If a question asks how much must be repaid, or the final balance, you must add the principal back — the interest alone is only a halfway answer.

What if the question gives me the interest and asks for the rate, time, or principal?

Use the same formula, SI = (P × R × T) ÷ 100, and substitute the three values you know, then solve for the missing one. For example, $450 interest on $P at 5% for 2 years gives 450 = P × 10 ÷ 100, so P = $4,500. Always check by plugging your answer back in.