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