Loans & Lump Sums
Loan payment (installment loan)
PMT =
P × (APR/n)1 − (1 + APR/n)−nY
P = amount borrowed. Note the negative exponent. This is different from the savings-plan formula.
Deposit needed now (present value)
P =
A(1 + APR/n)nY
Daily compounding: n = 365. Monthly: n = 12. Quarterly: n = 4.
Years to reach a target balance
Y =
log(A/P)n × log(1 + APR/n)
Monthly interest on a balance
Monthly interest = balance × APR12
Simple vs. compound interest
- Simple: interest paid only on the original principal.
- Compound: interest paid on principal plus earlier interest.
Stocks
P/E ratio = share priceearnings per share
⇒
EPS = share priceP/E
- P/E above its historical range → stock seems overpriced.
- P/E below its historical range → stock seems underpriced.
Budgeting
Convert everything to the same time period
- Weekly → monthly:
× 4 (when told 1 month = 4 weeks)
- Annual → monthly:
÷ 12 Semiannual → monthly: ÷ 6 Quarterly → monthly: ÷ 3
- Daily → annual:
× 365 Monthly → annual: × 12
Net monthly cash flow = monthly income − monthly expenses
Negative cash flow means spending more than you earn.
Percent of budget = category spendingincome × 100%
Compare that percent to the chart's national average for the person's age group.
Cost of a class vs. working = tuition + wages you give up
Statistics Concepts
- Qualitative: categories or labels (professions, colors). Quantitative: numbers you can count or measure (population, height).
- Sampling: simple random means every member has an equal chance (names drawn from a hat). Systematic means every k-th member. Stratified means you split into groups and sample from each. Convenience means whoever is easy to reach.
- Correlation: points rising left to right are positive, and falling is negative. Points close to a line mean a strong correlation, and loosely scattered points mean a weak one. No pattern means no correlation.
- Bar graphs: describe each group's trend separately (steady increase, peak then decrease, and so on).
Algebra Review
- Exponent rules:
am × an = am+n and a1/2 = √a
- Solving equations: undo operations in reverse order (add or subtract first, then multiply or divide). Check by plugging your answer back in.
Calculator Tips
- Write percents as decimals (4% → 0.04).
- Put whole exponents in parentheses:
^(12*19)
- Don't round until the final answer.