Cheat Sheet · Topic 3

Compute, don't memorize

Plug in your numbers and get the answer in either direction. The web tool solves for any variable; the Excel workbook is yours to keep.

▸ Open the Financial Formulas Calculator ▼ Download the Excel workbook

Key formulas (ALEKS dictionary)

The exact formulas the ALEKS test expects. Variable names match the on-screen reference so you can jump from this page to the dictionary without re-mapping anything.

Simple interest

I = Prt  ·  A = P(1 + rt)

No compounding. Use for short-term loans, T-bills, and most ALEKS warmup problems.

Compound interest

A = P(1 + r/n)nt

Discrete compounding. n = periods per year (annual = 1, monthly = 12, daily = 365).

Continuous compounding

A = Pert

The limit of compound interest as n → ∞. e ≈ 2.71828 is Euler's number.

Future value of an annuity

A = M[(1 + r/n)nt − 1] / (r/n)

A series of equal payments M compounded over nt periods. Use for monthly contributions to a retirement account.

Effective annual yield (APY)

Y = (1 + r/n)n − 1

What a savings account actually pays in a year, with compounding factored in. Use APY (not APR) to compare two accounts.

Loan amortization → Topic 4

M = P(r/12) / (1 − (1 + r/12)−12t)

In the dictionary but lives in Topic 4 (Loans) — see that topic's cheat sheet for the worked version.

Variable legend

Same names as the ALEKS dictionary so the formulas above read identically on the test.

P = principal  ·  I = simple interest  ·  r = annual interest rate (decimal)

t = time, in years  ·  A = future value or amount accumulated

n = compounding periods per year  ·  e = Euler's number (≈ 2.71828)

M = installment payment or periodic deposit  ·  Y = effective annual yield (APY)

Common compounding values of n

annually = 1  ·  semiannually = 2  ·  quarterly = 4

monthly = 12  ·  weekly = 52  ·  daily = 365

continuously → use A = Pert instead

Common slips

Forgot to convert the rate

5% goes into the formula as 0.05, not 5. Always.

Mixed up A and I

I is just the interest, A is principal + interest. ALEKS questions usually ask for A.

Months instead of years

t is in years. 18 months is 1.5, not 18. Convert before plugging in.

Compared APRs instead of APYs

Two accounts with different compounding schedules need APY for a fair compare. APR alone hides the compounding difference.

Savings

Key formulas (ALEKS dictionary)

Variable legend

Common compounding values of n

Common slips