Simple interest, the warmup formula.
Multiply principal by rate by time. That's it. Simple interest grows in a straight line — no compounding, no surprises.
You buy a 26-week Treasury bill at auction for $9,775. Six months later, it pays out $10,000. Why didn't they just sell it for $10,000 in the first place?
Because the $225 difference is the interest. The Treasury sells the bill at a discount; the discount is what you earn for lending them money for half a year. The simple interest formula tells you exactly what rate that worked out to — and that's the same formula behind every short-term note, CD, and warmup ALEKS problem in this topic.
Simple interest grows on a straight line.
Each year adds the same $50 of interest. The growth line is straight — that's what "simple" means. Compound interest in Lesson 3 will bend this line.
Simple interest is calculated only on the original principal: I = P × r × t. The accumulated amount is A = P(1 + rt).
Vocabulary you'll see in word problems
- Simple interest Interest computed only on the original principal. Doesn't compound.
- Linear growth Equal additions in equal time periods. The graph is a straight line.
- Treasury bill (T-bill) Short-term U.S. government debt — typically 4, 13, 26, or 52 weeks. Standard real-world use of simple interest.
- Term How long the principal is lent or invested, in years. Convert months and days to years before plugging into the formula.
- Accumulated amount (A) Principal plus interest. A = P + I, which factors to P(1 + rt).
A 6-month T-bill at 4.5% on $10,000.
"A 26-week Treasury bill has a face value of $10,000 and pays 4.5% simple interest. How much interest does it earn at maturity, and what's the total payout?"
Convert the time to years.
The formula expects t in years. 26 weeks is six months — half a year.
Convert the percent to a decimal.
Same step as Lesson 1. Drop the %, shift the decimal two places left.
Apply I = Prt.
Multiply principal by rate by time. All three pieces are now in compatible units: dollars, decimal rate, years.
Find the accumulated amount.
Either add interest to principal (A = P + I), or use the factored form A = P(1 + rt). Both give the same answer.
Sanity check.
4.5% per year on $10,000 is about $450 annually. Over half a year, around $225. The math agrees. If you'd computed $4,500 or $22.50, the decimal slipped on either the rate or the time.
Three problems. Different missing pieces. Same recipe.
Compute the simple interest on $5,000 at 8% annual for 2 years.
An 18-month note pays 4% simple interest on $4,000. What's the total at maturity? (Hint: 18 months in years.)
A $1,000 deposit at 4% simple interest earned $60. How many years was the deposit?
Three fast questions before you move on.
Q1. Simple interest is the right tool when...
Q2. Plotted over time, simple interest grows as a...
Q3. 9 months at 4% on $2,000. The interest is...
When simple interest is enough — and when it isn't.
Most short-term lending uses simple interest because the time is short enough that compounding wouldn't make a meaningful difference. A 90-day T-bill earning 4.5% pays a flat fraction of the principal at maturity. The math is fast, the answer is exact, no exponents needed.
The catch shows up over long horizons. $10,000 at 5% simple interest for 30 years pays $15,000 in interest. The same deposit with monthly compounding pays about $34,800 — more than double. Banks pay you compound interest because they earn compound interest on the loans they make with your deposit, and compounding is what makes long-term saving feel like magic. That's Lesson 3.
Next: compound interest, compounding frequency, and the continuous limit. The straight line you saw above starts to bend.
Continue to Lesson 03Different angle? Need another rep? These are optional — tap any that look helpful.