MAT-144 · Mathematical Reasoning
Topic 03 · Savings
Study card
The formulas, the moves, and the traps for Topic 3, in one printable page.
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.
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)
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
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.