What interest actually is.
Before any formula, four words: principal, rate, time, interest. Once you name them, every calculation in this topic becomes a recipe.
Your savings account paid you $34 last month. Your credit card statement shows you owe $52 in interest. Both are interest — same word, opposite directions. The math underneath is identical: a percentage of some starting amount, multiplied by how long it sat there.
By the end of this lesson you'll be able to name the four pieces every interest formula uses, no matter which direction the money is flowing. Naming them is the move that makes the rest of Topic 3 a recipe instead of a guess.
Interest is rent paid for borrowed money.
Every interest problem has the same four pieces. Principal × rate × time gives you the interest; principal plus interest gives you the future value.
Interest is the dollar amount paid for the use of money, calculated as a percentage of the principal over a specified term.
The four names you need
- Principal (P) The starting amount: what you borrowed or deposited. Every formula starts here.
- Rate (r) The annual interest rate, written as a decimal. 5% becomes 0.05 before it goes into a formula.
- Time (t) The term of the loan or investment, in years. Six months is 0.5; a decade is 10.
- Interest (I) The dollar amount of interest itself — the growth in the pile, separate from the principal.
- Future value (A) The whole pile after interest: principal plus interest. Most ALEKS questions ask for A, not I.
Lend a friend $500 at 6% for two years.
"Your friend asks to borrow $500 to fix their transmission. You agree on 6% annual interest, paid back in two years. How much will they owe you at the end?"
Name the four pieces.
P = $500 (the principal you lent). r = 6% (the rate). t = 2 years (the term). A = ? (what you'll get back, principal plus interest).
Convert the percent to a decimal.
The % symbol means "divide by 100." Shift the decimal two places to the left.
Compute the interest.
Interest equals principal times rate times time. Multiply across.
Add interest back to principal.
The future value is what your friend hands back: the original $500 plus the $60 of interest that accrued.
Sanity check.
6% of $500 is about $30 per year. Over two years, around $60 of interest. The total ($560) is a little more than the principal ($500). If you'd computed $830 or $20, the decimal slipped somewhere. Always pause and ask: does this answer feel right?
Three problems. Different missing pieces. Same recipe.
Deposit $1,000 at 5% annual interest for 1 year. How much interest do you earn?
A $2,000 deposit earns 4% annual simple interest for 3 years. What's the accumulated amount?
A $1,000 deposit earned $120 in simple interest over 2 years. What annual rate did it pay? Type just the number (e.g. 5 for 5%).
Three fast questions before you move on.
Q1. In an interest formula, 5% goes in as...
Q2. 9 months as a value of t in years is...
Q3. If a question asks "how much will they pay back?" they're asking for...
Why we name the pieces before we calculate.
Half the mistakes in this topic come from misreading the problem, not from getting the math wrong. Is the rate annual or monthly? Is the term in years or months? Is the question asking for I or for A? Naming the four pieces before you start anchors the rest.
Try this discipline on every interest problem the rest of the week: before you reach for a formula, write down P, r, t, and what's being asked for. Then pick the formula. Then plug in. The naming step takes ten seconds and saves the wrong answer from sneaking in.
Next: Lesson 02 picks the simplest formula in the topic — I = Prt — and shows when it's the right tool. Treasury bills, short-term notes, and most ALEKS warmup problems live here.
Different angle? Need another rep? These are optional — tap any that look helpful.