Every number in adult life is a percent of something, and the question is always which something. A pay stub read line by line: gross, withholding, FICA, net. Simple interest as a line and compound interest as an exponential, with the Rule of 72 and a logarithm for the exact doubling time. APR turned into a monthly rate, a loan amortized month by month, and two loans compared by total cost with the fee included. Credit cards, inflation, unit prices, tax brackets and a 50/30/20 budget. All numbers are invented examples, not advice. Study cards, hints, a practice quiz at three levels, and four workshop activities that check themselves.
A card says 6% APR. That number is for a whole YEAR, not for the month on your statement.
Match the rate to the period before you multiply. A yearly rate divided by 12 gives the monthly rate — and if you divide the rate, you must also multiply the number of periods, or the two halves of the formula stop agreeing.
What people get wrong
⚠️People often think…
A 6% APR on $10,000 costs $600 this month.
That is the whole year. One month is 6% ÷ 12 = 0.5%, which is $50. Always ask what period the rate is measured in before you touch the balance.
Divide the yearly rate by 12 first.
⚠️People often think…
8% tax on a $40 item makes it $48.
You added 8 dollars, not 8 percent. Percent means of the amount: 40 × 0.08 = $3.20, so $43.20. A percent is never dollars until it meets a number.
A percent is of something. Multiply.
⚠️People often think…
$1,000 at 5% for 10 years grows to $1,500.
That is simple interest — $50 a year, forever the same. Compounding earns on the interest too: 1,000 × 1.05¹⁰ = $1,628.89. The gap is the whole reason compounding matters.
Compound earns on the interest too.
⚠️People often think…
The loan with the lower monthly payment is the cheaper loan.
A smaller payment usually means more months. Only payment × number of months, plus fees, is the real cost — and by that measure the low payment often costs the most.
Payment times months, plus fees. That is the cost.
Rate per period, periods, then the total
1Watch one
What is one month of interest on $10,000 at 6% APR?
The rate is yearly, so cut it to one month: 6% ÷ 12 = 0.5%.
Write it as a decimal: 0.005.
Multiply by the balance: 10,000 × 0.005.
$50 for the month. The yearly total would be $600 — twelve times as much. ✓
2Do one with me
A $40 item with 8% tax; $1,000 at 5% compounded yearly.
The $40 item with tax costs
The monthly rate for a 6% APR is
The yearly growth factor for 5% is
💬One sentence, then you move on
Why is 8% tax not the same as adding 8 dollars?
3Try one
Loan A: $200 a month for 60 months. What is its total cost, before fees?
I want a hint first
Multiply the payment by how many times you make it: 200 × 60.
💬Last one — then you're done here
Why can a loan with a smaller payment cost more?
Where this goes
Where this lives
A first paycheck, a card statement, a car loan, a savings account. Every one of them is a rate meeting a period — and the person who checks which period wins.
What this feeds
Next is the capstone, where you build a model of your own and defend it.
One card at a time — tap “Show me” to check yourself, then Next. Start at Foundation; when those feel easy, climb.
Helpful Hints
🧭 Any interest question — the routine
Find the rate PER PERIOD (APR ÷ 12 for monthly) and the NUMBER of periods (years × 12). Simple interest: add P × r × t once. Compound: multiply by (1 + rate per period) once per period — A = P(1 + r/n)ⁿᵗ. For a loan, run it month by month: interest = balance × monthly rate, principal = payment − interest, new balance = old balance − principal. Then always finish with the TOTAL: payments × months + fees.
Rate per period, periods, then the total.
💡 The whole unit in one idea
Every number here is a percent of something, and the question is always WHICH something. Simple interest is a percent of the original amount — a line. Compound interest, inflation and credit-card debt are a percent of the CURRENT amount — an exponential, which is why they run away from a line over time. A paycheck, a budget, a loan and a tax bracket are each just a chain of “percent of what?” done in the right order. All numbers in this room are invented examples, not advice.
⚠️ Traps the test loves
Applying the yearly APR to one month. 6% APR is 0.5% a month: $50 on $10,000, not $600.
Adding a percent as dollars: $40 + 8 for 8% tax. It is 40 × 1.08 = 43.20.
Simple where it should be compound: 1,000 + 10 × 50 = 1,500 instead of 1,000 × 1.05¹⁰ = 1,628.89.
Dividing the rate by 12 without multiplying the exponent by 12, or the reverse.
Judging a loan by its rate or its payment. Only payments × months + fees is the cost.
Believing a raise into a higher bracket cuts take-home pay. Only the dollars above the line pay the higher rate.
📐 The formulas — the chart
Question
Formula
Worked example
Net pay
gross − withholding − FICA − state
2,000 − 180 − 153 − 60 = 1,607
FICA
7.65% × gross
0.0765 × 2,000 = 153
Simple interest
A = P(1 + rt)
1,000(1 + 0.05 × 10) = 1,500
Compound, yearly
A = P(1 + r)ᵗ
1,000 × 1.05¹⁰ = 1,628.89
Compound, monthly
A = P(1 + r/12)¹²ᵗ
1,000(1 + 0.05/12)¹²⁰ = 1,647.01
Doubling time
≈ 72 ÷ rate; exactly ln 2 ÷ ln(1 + r)
5%: ≈ 14.4; exactly 14.2 years
Loan payment
M = P·r ÷ (1 − (1 + r)⁻ⁿ)
10,000, r = 0.005, n = 36 → 304.22
One month of a loan
interest = balance × r; principal = M − interest
50.00; 254.22; balance 9,745.78
Total cost
M × n + fees
36 × 304.22 = 10,951.92
🎯 How the test will ask
A pay stub — “find the net pay” or “what percent is FICA?” Gross first, then subtract each line.
A deposit, a rate and a time — “simple or compound, how much?” Decide which, then the formula.
“How long to double?” Rule of 72 to estimate, a logarithm to be exact.
A loan’s first months — “fill in the table.” Interest, principal, balance; repeat.
Two loans — “which is cheaper?” Total cost of each, fees included, over the actual term.
A credit card and a minimum payment — “what is the balance after a month?” Add the interest first, then subtract the payment.
A budget — “does this goal fit?” Goal ÷ months, then compare with the savings slice.
✅ Before the test, can you…
Read a pay stub and compute the net pay from the gross and the deductions?
Find a percent of a number, add a tax, take a discount, and compute a percent change?
Tell simple from compound interest and compute both for $1,000 at 5% over 10 years?
Convert an APR to a monthly rate and work the first two months of a loan?
Compare two loans by total cost, fees included?
Explain why a minimum payment barely moves a credit-card balance?
Build a 50/30/20 budget from a take-home amount and test a savings goal against it?
Pick your level
Look back at anything you missed — the hint that appeared is exactly what to reread tonight.
How sure did you feel?
Workshop
Work like someone who reads the fine print: label the four numbers on a pay stub, put the first months of a loan in order, graph simple against compound interest and watch the gap open, then argue which of two loans really costs less. Every number here is an invented example, not advice. Every activity checks itself, and hints are free.
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