MAT-144 · Mathematical Reasoning
Topic 03 · Savings
Vocabulary & key terms
Every term defined across this topic, grouped by lesson. Tap a lesson title to jump back to the page where the term was introduced.
30
terms in this topic. Skim before the review.
Course tool
Pick one of the seven ALEKS dictionary formulas, pick which variable is missing, fill in the rest. Includes a downloadable Excel workbook.
- 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.
- 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).
- Compound interest
- Interest paid on principal plus previously earned interest. The pile grows on itself.
- Compounding period
- The interval at which interest is added to the principal. Annual, monthly, daily, or continuous.
- Compounding frequency (n)
- Number of compounding periods per year. Annual = 1, semiannual = 2, quarterly = 4, monthly = 12, daily = 365.
- Continuous compounding
- The limit case where interest is added instantaneously and continuously. Uses A = Pert.
- Euler's number (e)
- An irrational constant, approximately 2.71828. Appears whenever something grows or decays continuously.
- APY (Effective Annual Yield)
- What an account actually pays in a year, with compounding factored in. Always ≥ APR for any n > 1.
- APR (Nominal rate)
- The advertised annual rate, before compounding effect. Also called the stated or nominal rate.
- CPI (Consumer Price Index)
- The U.S. Bureau of Labor Statistics index tracking the cost of a basket of household goods. The data source for inflation.
- Inflation
- The annual percent increase in prices. Computed from CPI: (CPInew / CPIold) − 1.
- Nominal vs. real return
- Nominal is the headline rate. Real is what's left after subtracting inflation. Real is what your purchasing power actually did.
- Lump sum
- One deposit, left to grow. Future value comes from the compound interest formula.
- Annuity
- A series of equal periodic payments — weekly, monthly, or annually — into a savings or investment account.
- Periodic payment (M)
- The amount of each regular deposit. The ALEKS dictionary uses M; some textbooks use PMT.
- Future value (A)
- What the lump sum or annuity will be worth at the end of the time horizon.
- Time horizon
- How long the money has to grow. Lengthening t beats raising r for long-term saving.
- Emergency fund
- 3 to 6 months of expenses, kept liquid. The first savings goal — before any longer-term investing makes sense.
- HYSA (high-yield savings account)
- An online savings account paying APYs near the federal funds rate. Where short-term savings live.
- CD (certificate of deposit)
- A time deposit with a fixed term and rate. Can't withdraw early without penalty. Used for mid-term goals.
- IRA / 401(k)
- Retirement accounts with tax advantages. Where long-term savings compound for decades. Topic 7 covers what to put inside them.
- Time horizon
- How long until you need the money. The single biggest factor in choosing a vehicle and a formula.