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CELE Engineering Mathematics — Engineering EconomyMemory Anchors

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Memory anchors for Engineering Economy reviewers. When plain memorisation is not enough, these mnemonic devices help you lock in the key concepts for the CELE 2026. Tested against the kinds of questions Professional Regulation Commission (PRC) — Board of Civil Engineering actually uses in CELE Engineering Mathematics.

Exam context

For the Civil Engineer Licensure Examination, Professional Regulation Commission (PRC) — Board of Civil Engineering tests Engineering Mathematics under a "Core" label, with Engineering Economy in the 10th slot across 10 chapters. CELE candidates must clear the 70% weighted average, no sub-test below 50% cut on the 2026 paper, which draws about a meaningful share of Engineering Mathematics questions. Date to watch: May and November 2026.

Engineering Economy - Memory Anchors

Memory techniques can increase long-term recall by up to 400% compared to passive reading. For Engineering Economy, you must instantly recall formulas, know which one to apply, and execute calculations under time pressure. These memory anchors use mnemonics, vivid analogies, micro-stories, and visual associations to wire every key formula and concept into your long-term memory. Filipino cultural references and board-exam-style triggers are woven throughout. Study each anchor, close your eyes, and replay the story or image — the goal is that when you see '₱10,000 compounded at 8% for 5 years,' the formula fires automatically, not after 30 seconds of searching your notes.

Anchors

Topic

Compound Interest

Concept

Compound Interest Formula: F = P(1+i)^n

Anchor Id

Difficulty

easy

Memory Aid

Imagine a Pinoy OFW named FRANK who left ₱10,000 with his nanay before flying to Riyadh. Every year, his money grows by a little bit (1+i), and this happens n times. When he comes back after n years, he asks: 'Frank, how much is my money?' FRANK = Future (F) equals Present (P) times the growth factor (1+i) raised to the number of years (n). FRANK grew exponentially, just like the formula: F = P(1+i)^n. The OFW grows richer the longer he stays abroad — the longer n is, the bigger (1+i)^n becomes.

Anchor Type

micro_story

Why It Works

The micro-story ties the variables F, P, i, n to a relatable Filipino OFW narrative. The character name FRANK directly cues 'Future' and the story reinforces that time (n) is the exponent — the most commonly confused part of the formula.

Example Usage

Board question: 'Find F for P=₱10,000, i=8%, n=5 years.' Trigger: FRANK the OFW. Write F = P(1+i)^n = 10,000(1.08)^5 = ₱14,693.

Recall Trigger

Think of FRANK the OFW. His money grew n times at rate (1+i).

Topic

Present Worth / Discounting

Concept

Present Worth Formula: P = F(1+i)^(-n) — discounting future money back

Anchor Id

Difficulty

easy

Memory Aid

Think of a BUKO PANDAN dessert at a birthday party two weeks from now. That future dessert is worth ₱500 then (F), but if you want its value TODAY (P), you have to 'discount' it — meaning its present worth is less because you don't have it yet. The negative exponent (-n) is the DISCOUNT — it shrinks the future value back to today. 'P is the price you'd pay today for something you'll receive in the future.' Negative power = punting backward in time. The deeper you discount (larger n), the smaller P becomes.

Anchor Type

analogy

Why It Works

The food analogy is concrete and immediately relatable. The 'negative exponent = discount' association is a direct conceptual hook that prevents the common mistake of using a positive exponent for present worth.

Example Usage

Board question: 'Find P for F=₱50,000 due in 8 years at 12%.' Write P = 50,000(1.12)^(-8) = 50,000 × 0.4039 = ₱20,196.

Recall Trigger

Discounting = negative exponent. Shrink F back to P using (1+i)^(-n).

Topic

Nominal vs Effective Interest Rate

Concept

Effective Interest Rate: i_eff = (1 + r/m)^m - 1

Anchor Id

Difficulty

medium

Memory Aid

Remember the phrase: 'Rate Over M, Raised to M, Minus 1.' Acronym: RORMM1. Say it aloud: 'arr-oh-arr-em-em-one.' This maps directly: (r/m) is 'Rate Over M,' the whole bracket is raised to the power m, then subtract 1. The minus-one strips away the original principal so you're left with just the INTEREST earned. Think: the more times you compound (bigger m), the more effective the rate — like a sari-sari store owner who reinvests profits daily versus monthly.

Anchor Type

mnemonic

Why It Works

The rhythmic acronym RORMM1 encodes the formula structure in the correct left-to-right order. The sari-sari store analogy reinforces the concept that higher compounding frequency increases the effective rate.

Example Usage

Board question: 'Find i_eff for r=12% compounded monthly.' m=12. i_eff = (1 + 0.12/12)^12 - 1 = (1.01)^12 - 1 = 1.1268 - 1 = 12.68%.

Recall Trigger

RORMM1 — Rate Over M, Raised to M, Minus 1.

Topic

Annuity — Future Worth

Concept

Annuity Future Worth: F = A[(1+i)^n - 1] / i

Anchor Id

Difficulty

medium

Memory Aid

Imagine ANNA (A = uniform deposit, like an 'Annuity') drops ₱1,000 every end of month into a piggy bank that earns interest. At the END of all n months, she smashes the piggy bank. What comes out? The Future worth (F). The formula factor [(1+i)^n - 1] / i is called the 'FUSA factor' (Future-Uniform-Series-Amount). ANNA's piggy bank grows by this factor. Key: if A is the deposit and i is the rate, F = A × FUSA. Smashing the bank at end = Future Worth.

Anchor Type

micro_story

Why It Works

Giving the series factor a name (FUSA) and a character (ANNA) creates dual encoding — verbal and narrative. The 'smashing the piggy bank' image creates a vivid endpoint that reminds students this formula gives the FUTURE worth.

Example Usage

Board question: 'Monthly deposits of ₱2,000 for 36 months at 0.5%/month. Find F.' F = 2000 × [(1.005)^36 - 1]/0.005 = 2000 × 39.336 = ₱78,671.

Recall Trigger

ANNA smashes the piggy bank at the end — F = A × FUSA = A[(1+i)^n-1]/i.

Topic

Annuity — Present Worth

Concept

Annuity Present Worth: P = A[(1+i)^n - 1] / [i(1+i)^n]

Anchor Id

Difficulty

medium

Memory Aid

The Present Worth of an annuity formula is the Future Worth formula with an extra (1+i)^n in the denominator. Think of it this way: to get the Present Worth, you take the Future Worth factor and DIVIDE it by (1+i)^n — you 'pull it back to today' by that extra discount. The denominator has TWO parts: i × (1+i)^n. Picture a fraction: the numerator is the same as the FUSA factor, but the denominator is FUSA's denominator MULTIPLIED by one more (1+i)^n. Memory tip: P formula = F formula denominator gets an upgrade — multiply i by (1+i)^n.

Anchor Type

analogy

Why It Works

Connecting the P-annuity formula to the F-annuity formula (which students already know) reduces cognitive load. The 'denominator upgrade' framing makes the structural difference immediately visible.

Example Usage

Board question: 'Find P for A=₱1,000/yr, i=10%, n=5.' P = 1000×[(1.10)^5-1]/[0.10×(1.10)^5] = 1000×0.6105/[0.10×1.6105] = 1000×3.791 = ₱3,791.

Recall Trigger

P-annuity = F-annuity factor, but denominator gets extra (1+i)^n. Denominator upgrade.

Topic

Perpetuity

Concept

Perpetuity: P = A/i

Anchor Id

Difficulty

easy

Memory Aid

A PERPETUITY is like a scholarship fund at UP Diliman that pays students FOREVER. The school endows ₱1,000,000 (P), it earns interest at rate i, and every year gives out A = P×i pesos to scholars. Rearranged: P = A/i. It's the SIMPLEST formula in Engineering Economy — just divide the annual payment by the interest rate. No exponents, no fancy factors. Think: 'Permanent Payment = A divided by i.' The UP scholarship pays PERMANENTLY, so the formula is permanently simple.

Anchor Type

analogy

Why It Works

The scholarship analogy is culturally resonant for Filipino students. Emphasizing that perpetuity has the SIMPLEST formula (no exponents) prevents students from overcomplicating it in the exam.

Example Usage

Board question: 'What endowment gives ₱50,000/yr forever at 8%?' P = A/i = 50,000/0.08 = ₱625,000.

Recall Trigger

UP scholarship forever = A/i. Perpetual, permanent, plain simple.

Topic

Straight-Line Depreciation

Concept

Straight-Line Depreciation: d = (C - S)/n

Anchor Id

Difficulty

easy

Memory Aid

The acronym is CSN: Cost minus Salvage over N. Pronounce it like 'Season' (CSN). 'Every season, the machine loses its value equally.' The formula is as straight as a ruler — that's why it's called STRAIGHT-LINE. Every year, the machine loses the same fixed amount: d = (C-S)/n. Book value at year t: BV_t = C - d×t. Picture drawing a straight LINE on a graph from C (at year 0) down to S (at year n). That line's slope is the annual depreciation d.

Anchor Type

mnemonic

Why It Works

CSN as 'season' is phonetically sticky. The visual of a straight downward line directly maps to the concept name 'straight-line' and encodes that depreciation is constant each period.

Example Usage

Board question: 'Machine costs ₱100,000, salvage ₱10,000, life 5 years. Find d and BV₃.' d = (100,000-10,000)/5 = ₱18,000/yr. BV₃ = 100,000 - 3×18,000 = ₱46,000.

Recall Trigger

CSN = Cost minus Salvage over N. Straight line down every season.

Topic

SYD Depreciation

Concept

Sum-of-Years-Digits (SYD) Depreciation — accelerated, higher in early years

Anchor Id

Difficulty

hard

Memory Aid

Imagine a brand-new car (like a Toyota Vios bought in Manila). The moment you drive it off the showroom, it loses the MOST value — Year 1 depreciation is the HIGHEST. Each subsequent year, it loses less. That's SYD: front-loaded depreciation. The SYD denominator is the SUM OF ALL YEAR NUMBERS: for n=5, SYD = 1+2+3+4+5 = 15. Year 1 fraction = 5/15 (remaining life at START of year over SYD). Year 2 = 4/15, etc. The fractions DECREASE each year, like the car's value dropping fast then slowing. Formula: d_t = (n - t + 1)/SYD × (C - S).

Anchor Type

micro_story

Why It Works

The brand-new car analogy is universally understood in the Philippines (Toyota Vios is a common reference). The decreasing fractions map directly to the decreasing year numerators in SYD.

Example Usage

Board question: 'SYD depreciation Year 1 for machine C=₱250,000, S=₱25,000, n=8.' SYD=36. d₁ = 8/36 × (250,000-25,000) = 8/36 × 225,000 = ₱50,000.

Recall Trigger

New Vios loses most value in Year 1. SYD = sum of 1 to n. Year t uses (n-t+1) in numerator.

Topic

Period Consistency — Board Exam Pitfall

Concept

Period Consistency — i and n must match the same compounding period

Anchor Id

Difficulty

medium

Memory Aid

Think of BOXING: a boxer's weight is measured in the SAME weight class. You can't have a boxer fight in two different weight classes simultaneously. Similarly, if the problem says '12% compounded MONTHLY,' you CANNOT use i=12% and n=years. You must convert: i = 12%/12 = 1%/month and n = number of MONTHS. Always fight in the SAME weight class. Monthly rate with monthly periods. Annual rate with annual periods. Mixing them is a knockout — you get the wrong answer.

Anchor Type

analogy

Why It Works

The boxing weight-class analogy creates a binary pass/fail mental check. Filipino students are familiar with boxing (Manny Pacquiao is a national icon), making this culturally sticky.

Example Usage

Problem says '6% compounded monthly for 3 years.' Use i=0.06/12=0.5%/month and n=36 months, NOT i=6% and n=3.

Recall Trigger

Pacquiao's weight class — i and n must be in the SAME compounding period.

Topic

Annuity Types — Timing

Concept

Ordinary Annuity vs Annuity-Due (timing of payments)

Anchor Id

A10

Difficulty

medium

Memory Aid

Picture a JEEPNEY and its passengers. In an ORDINARY annuity, passengers pay at the END of the ride (pagtapos). In an ANNUITY-DUE, passengers pay at the START (pagsakay). The payment timing shifts all cash flows by one period earlier for annuity-due. For annuity-due: multiply the ordinary annuity factor by (1+i). Visual: draw a timeline. Ordinary: arrows at END of periods 1,2,3...n. Annuity-due: arrows at BEGINNING of periods 1,2,3...n (i.e., at times 0,1,2...n-1).

Anchor Type

visual_association

Why It Works

The jeepney is a quintessentially Filipino image. The pang-ordinary = bayad sa dulo (pay at end) association is direct and reversible. The (1+i) multiplier for annuity-due follows logically from 'one period earlier = one period more growth.'

Example Usage

If a problem says 'deposits at the beginning of each year,' it is annuity-due. P_due = P_ordinary × (1+i).

Recall Trigger

Jeepney: ordinary = bayad sa dulo (end). Annuity-due = bayad sa simula (start). Multiply by (1+i).

Topic

Simple Interest

Concept

Simple Interest: F = P(1 + in)

Anchor Id

A11

Difficulty

easy

Memory Aid

Simple interest is 'PINE': P times (1 + i times n). The word PINE has four letters: P-I-N-E. P = Principal, I = interest rate, N = number of periods, E = the formula END result? No — think of PINE as the INPUTS: Principal, Interest rate, Number of periods, Everything multiplied simply. Unlike compound interest (exponent), simple interest just multiplies: i×n is LINEAR, not exponential. 'PINE grows straight up' — a pine tree grows linearly, unlike an exponential curve.

Anchor Type

mnemonic

Why It Works

PINE encodes the four key elements (P, i, n, 1+in) and the 'straight tree' visual reinforces the LINEAR (non-exponential) nature of simple interest. This prevents students from accidentally using the compound formula.

Example Usage

Board question: '₱5,000 at 8% simple interest for 3 years. Find F.' F = 5,000(1 + 0.08×3) = 5,000(1.24) = ₱6,200.

Recall Trigger

PINE tree grows straight (linear). F = P(1+in) — simple, straight.

Topic

Benefit-Cost Ratio

Concept

Benefit-Cost Ratio (B/C) — project is justified if B/C ≥ 1

Anchor Id

A12

Difficulty

easy

Memory Aid

Think of a TAHO vendor analyzing whether to expand. He spends ₱500/day in costs (C) and earns ₱700/day in benefits (B). B/C = 700/500 = 1.4 > 1. JUSTIFIED — expand! If B/C < 1, the costs outweigh the benefits — like spending ₱700 to earn only ₱500. That's a bad investment. The rule: B/C ≥ 1 = GO. B/C < 1 = NO. Simple as a taho vendor's daily math. For government projects (like DPWH roads), B/C analysis is required — benefits include social value, not just profit.

Anchor Type

analogy

Why It Works

The taho vendor is a universally recognizable Filipino street vendor. The GO/NO binary makes the criterion immediately actionable. Mentioning DPWH connects to real-world Philippine engineering practice.

Example Usage

Board question: 'B = ₱2.5M, C = ₱2.0M. Is the project justified?' B/C = 2.5/2.0 = 1.25 > 1. YES, justified.

Recall Trigger

Taho vendor: B/C ≥ 1 = GO (expand). B/C < 1 = NO (don't expand).

Topic

Break-Even Analysis

Concept

Break-Even Analysis — point where two alternatives cost the same

Anchor Id

A13

Difficulty

medium

Memory Aid

Two construction companies bid for a project: Company A has high fixed cost but low variable cost (mechanized). Company B has low fixed cost but high variable cost (manual labor). At LOW production, B is cheaper. At HIGH production, A is cheaper. They BREAK EVEN at some output level. Visualize it as two jeepney routes that cross at one intersection — before the crossing, one is shorter; after, the other is. The crossing point is BREAK-EVEN. To find it: set Cost_A = Cost_B and solve for the unknown (volume, time, etc.).

Anchor Type

micro_story

Why It Works

The two-route jeepney visual creates a spatial memory of lines crossing. Setting two equations equal is a fundamental algebraic operation that students already know — the story just anchors WHEN to use it.

Example Usage

Machine A: FC=₱100,000, VC=₱5/unit. Machine B: FC=₱60,000, VC=₱9/unit. Break-even: 100,000+5Q=60,000+9Q → Q=10,000 units.

Recall Trigger

Two jeepney routes crossing at one point — that intersection is Break-Even. Set Cost_A = Cost_B.

Topic

Nominal vs Effective Rate

Concept

Nominal Rate (r) vs Effective Rate (i_eff) — r is STATED, i_eff is ACTUAL

Anchor Id

A14

Difficulty

medium

Memory Aid

The NOMINAL rate is like a politician's PROMISED salary (they say ₱30,000/month). The EFFECTIVE rate is what you ACTUALLY take home after all the compounding bonuses. The more often compounding happens, the bigger the gap between nominal and effective. '12% compounded monthly' is the PROMISE (nominal). The actual effective rate is 12.68% — higher because of monthly compounding. Rule: NOMINAL = NAMED (the rate AS NAMED in the problem). EFFECTIVE = EARNED (what you ACTUALLY earn). Always convert to effective before comparing alternatives across different compounding frequencies.

Anchor Type

analogy

Why It Works

The promised-vs-actual salary analogy resonates with Filipino workers aware of salary deductions and allowances. N for Nominal = Named is a direct letter-to-concept link. E for Effective = Earned reinforces the actual value concept.

Example Usage

Two banks: Bank A offers 12% compounded monthly, Bank B offers 12.5% compounded annually. Compare using i_eff. Bank A: i_eff=(1.01)^12-1=12.68%. Bank B: i_eff=12.5%. Choose Bank A.

Recall Trigger

Nominal = Named (stated). Effective = Earned (actual). Always use Effective for comparisons.

Topic

Book Value — Straight-Line

Concept

Book Value Formula: BV_t = C - d×t (Straight-Line)

Anchor Id

A15

Difficulty

easy

Memory Aid

Draw a STRAIGHT LINE on your mental screen. Left axis: value in pesos. Bottom axis: years. The line starts at the TOP LEFT at height C (cost) and goes DOWN at constant slope d (annual depreciation) until it hits the bottom right at height S (salvage) after n years. At any year t, the book value BV_t is where the line IS at that moment — you just go along the line. BV_t = C - d×t. The 'book' in book value = the accounting record. Imagine the machine's value written in a ledger book, decreasing by d pesos every year in a perfectly straight column.

Anchor Type

visual_association

Why It Works

The straight-line graph is a direct visual representation of the concept name. Drawing it mentally creates spatial memory. The ledger book image reinforces the accounting context of 'book value.'

Example Usage

d=₱18,000/yr. BV₃ = 100,000 - 18,000×3 = 100,000 - 54,000 = ₱46,000.

Recall Trigger

Picture the straight line descending from C to S. Year t is d×t steps down from C.

Topic

Rate of Return

Concept

Rate of Return (ROR) — the interest rate at which PW of benefits = PW of costs

Anchor Id

A16

Difficulty

hard

Memory Aid

ROR is like asking: 'What interest rate would a bank need to offer so that this project and a bank deposit give the same result?' If the project's ROR exceeds the MARR (Minimum Attractive Rate of Return), choose the project. Think of it as comparing your Pagibig Fund return rate versus a private investment. If your private investment's ROR > Pagibig rate, invest privately. ROR = the project's internal 'PAGIBIG RATE' — if it beats the minimum acceptable, it's worth doing.

Anchor Type

analogy

Why It Works

Pag-IBIG Fund is immediately recognizable to Filipino professionals as a mandatory savings program. Framing ROR as the 'project's Pag-IBIG rate' creates a concrete benchmark comparison.

Example Usage

If MARR=10% and project ROR=15%, the project is economically justified. Find ROR by trial and error: set PW of costs = PW of benefits and solve for i.

Recall Trigger

ROR = project's Pag-IBIG rate. If ROR > MARR, take the project.

Topic

Declining Balance Depreciation

Concept

Declining Balance Depreciation — constant RATE applied to book value, not cost

Anchor Id

A17

Difficulty

hard

Memory Aid

Imagine a LEAKING DRUM of water. Every day, the drum loses 20% of WHATEVER WATER REMAINS (not 20% of the original full drum). Day 1: 1000L × 20% = 200L lost, 800L remains. Day 2: 800L × 20% = 160L lost. Day 3: 640L × 20% = 128L lost. The leak rate (d) is constant, but the AMOUNT lost decreases each day because the drum keeps getting less full. This is DECLINING BALANCE — the depreciation rate is fixed, but it's always applied to the CURRENT book value. BV_t = C(1-d)^t. The drum never fully empties (it asymptotes to zero, like salvage ≈ 0 for DB).

Anchor Type

micro_story

Why It Works

The leaking drum is a physical, visual, dynamic analogy. The 'decreasing amount lost each period' directly illustrates why DB is accelerated but self-limiting. The asymptote explanation addresses why DB never fully depreciates to zero.

Example Usage

Machine C=₱100,000, DB rate=40%. BV₁=100,000(0.60)=₱60,000. BV₂=60,000(0.60)=₱36,000. BV₃=36,000(0.60)=₱21,600.

Recall Trigger

Leaking drum losing fixed % of what remains. BV_t = C(1-d)^t.

Topic

Annual Worth Method

Concept

Annual Worth Method — comparing alternatives on equal annual cost basis

Anchor Id

A18

Difficulty

medium

Memory Aid

Think of two cellphone plans: Plan A costs ₱1,500/month flat. Plan B costs ₱800/month plus a ₱10,000 phone deposit. To compare fairly, convert Plan B's deposit into an equivalent monthly cost (₱10,000 × capital recovery factor). Now both plans are in 'monthly terms' — you're comparing APPLES to APPLES. This is the Annual Worth method: convert ALL costs (lump sums, gradients, whatever) into a single UNIFORM ANNUAL COST. Choose the lower Annual Worth (for costs) or higher Annual Worth (for benefits). The 'annualized plan' wins if it's the cheapest per year.

Anchor Type

analogy

Why It Works

Cellphone plans are immediately relatable to Filipino millennials and Gen Z. The 'apples to apples' framing reinforces why annual worth is valid — it normalizes all cash flows to the same basis for comparison.

Example Usage

Machine A: P=₱500,000, life=5 yr, i=10%. AW = 500,000 × (A/P, 10%, 5) = 500,000 × 0.2638 = ₱131,900/yr.

Recall Trigger

Cellphone plan comparison — convert everything to annual cost. Apples to apples.

Topic

SYD — Sum Calculation

Concept

SYD Sum Formula: SYD = n(n+1)/2

Anchor Id

A19

Difficulty

medium

Memory Aid

The SYD sum is just TRIANGULAR NUMBERS. For n=5: 1+2+3+4+5 = 15. The formula is n(n+1)/2 — the same as the formula for sum of first n integers (like the handshake problem). Mnemonic: 'N times N-plus-one, all over TWO.' Rhyme: 'N and N+1, multiply, then halve, you're done!' Alternatively: SYD = n(n+1)/2 is identical to the number of handshakes in a group of n+1 people. For n=8: SYD = 8×9/2 = 36. Quick check: n=4 → 4×5/2=10 ✓ (1+2+3+4=10).

Anchor Type

mnemonic

Why It Works

Connecting SYD sum to the triangular number formula (which students already know from arithmetic progressions) eliminates the need to memorize a new formula. The rhyme provides an additional phonetic memory hook.

Example Usage

n=8 years. SYD = 8×9/2 = 36. Year-1 SYD depreciation fraction = 8/36.

Recall Trigger

Triangular number: N times N+1, halved. SYD = n(n+1)/2.

Topic

Present Worth Method

Concept

Present Worth Method — choose the alternative with the HIGHEST net present worth

Anchor Id

A20

Difficulty

medium

Memory Aid

Imagine a CASHIER'S SCALE at a palengke. On the left pan, place all the COSTS (as present values — they are negative weights). On the right pan, place all the BENEFITS (as present values — positive weights). The NET present worth is how much one pan outweighs the other. If benefits outweigh costs, NPW > 0 — the project is worth doing. Among competing alternatives, pick the one whose scale tips MOST toward benefits (highest NPW). The scale image makes 'net present worth' physical and visual — you're literally weighing the money.

Anchor Type

visual_association

Why It Works

The palengke scale is immediately visualizable and culturally Filipino. The physical weighing metaphor makes the mathematical comparison (PW_benefits - PW_costs) intuitive and helps students remember that higher NPW = better alternative.

Example Usage

Alt A: NPW = +₱150,000. Alt B: NPW = +₱200,000. Choose Alt B (higher NPW).

Recall Trigger

Palengke scale — weigh PW benefits vs PW costs. Highest NPW wins.

Revision Game

F = P(1+i)^n — Compound Interest Future Worth

Clue

I am the OFW formula. I take your money today, multiply it by a growing factor, and return it bigger after n trips abroad. Who am I?

Memory Link

A1 — FRANK the OFW micro-story

Effective Interest Rate formula: i_eff = (1 + r/m)^m - 1

Clue

I am the formula that says: 'Rate Over M, Raised to M, Minus 1.' I convert a promise into reality. What is my name?

Memory Link

A3 — RORMM1 mnemonic

Annuity Future Worth: F = A[(1+i)^n - 1]/i

Clue

ANNA deposits ₱1,000 every month into my piggy bank. After 12 months, she smashes it open. I tell her how much is inside. Which formula am I?

Memory Link

A4 — ANNA and the FUSA piggy bank

Perpetuity: P = A/i

Clue

I am the simplest Engineering Economy formula — no exponents, no series factors. An endowment uses me to fund a scholarship FOREVER. What is my equation?

Memory Link

A6 — UP scholarship analogy

BV₃ = 100,000 - 3(18,000) = ₱46,000. Formula: BV_t = C - d×t

Clue

Tito Boy bought a machine for ₱100,000. It depreciates by ₱18,000 every year (CSN!). After 3 years, what is its book value?

Memory Link

A7 and A15 — CSN mnemonic and straight-line visual

Sum-of-Years-Digits (SYD). Denominator = n(n+1)/2. Year 1 numerator = n (highest).

Clue

A new Toyota Vios loses the MOST value in its first year. Which depreciation method does this describe, and what is the denominator formula?

Memory Link

A8 — new Vios micro-story, A19 — triangular number mnemonic

Break-Even Point. Set Cost_A = Cost_B and solve for the unknown variable (units, time, etc.)

Clue

Two companies have different cost structures and their costs are equal at exactly 10,000 units of production. What is this point called, and how do you find it?

Memory Link

A13 — two jeepney routes crossing

Correct. B/C < 1 means costs outweigh benefits. The taho vendor would be spending ₱85 to earn only ₱85 worth of benefit... wait — spending more than earning. Project is NOT justified.

Clue

A project's B/C ratio is 0.85. The DPWH engineer says 'reject.' Is she correct, and why?

Memory Link

A12 — taho vendor B/C analogy

BV_t = book value at end of year t; C = original cost; d = fixed depreciation rate per period (as a decimal); t = number of periods. Note: DB rarely reaches zero — salvage is inherent in the formula.

1. PERIOD MISMATCH — i and n not in same unit
2. NOMINAL vs EFFECTIVE confusion — using r instead of i_eff
3. ANNUITY TIMING — ordinary (end) vs annuity-due (start)
4. SALVAGE OMISSION — forgetting to subtract S in SL/SYD depreciation
5. SIGN ERRORS — costs negative, benefits positive in NPW

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CELE Engineering Mathematics — Engineering EconomyMemory Anchors

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Engineering Economy - Memory Anchors

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Memory Aid

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Why It Works

Example Usage

Recall Trigger

Tags

Topic

Concept

Anchor Id

Difficulty

Memory Aid

Anchor Type

Why It Works

Example Usage

Recall Trigger

Tags

Topic

Concept

Anchor Id

Difficulty

Memory Aid

Anchor Type

Why It Works

Example Usage

Recall Trigger

Tags

Topic

Concept

Anchor Id

Difficulty

Memory Aid

Anchor Type

Why It Works

Example Usage

Recall Trigger

Tags

Topic

Concept

Anchor Id

Difficulty

Memory Aid

Anchor Type

Why It Works

Example Usage

Recall Trigger

Tags

Topic

Concept

Anchor Id

Difficulty

Memory Aid

Anchor Type

Why It Works

Example Usage

Recall Trigger

Tags

Topic

Concept

Anchor Id

Difficulty

Memory Aid

Anchor Type

Why It Works

Example Usage

Recall Trigger

Tags

Topic

Concept

Anchor Id

Difficulty

Memory Aid