irori — Learning Worlds · DLP Edition

From a Cent, to a Million

Teacher's Answer Key

Full worked solutions for all 12 questions, with the formula substitution shown at each step, model answers for the open-ended parts, and a "watch for" note flagging the mistake students most often make on that question.

📐 Matches the DLP student edition exactly 🖨️ Printable

iroriBefore You Mark

A Few Notes Before You Use This Key

Rounding: final answers below are rounded to 2 decimal places (RM/sen or %) unless the working clearly produces a whole number. Accept any reasonable rounding a student carries through consistently from their own working.

Method marks: for every question, a correct formula with correct substitution but a small arithmetic slip should still receive the majority of method marks — these questions are designed to test whether the student picked the right approach (which formula, which variables, whether to rearrange), not pure calculator accuracy.

On Question 1: the $14 and $200 NVIDIA figures are real, rounded, split-adjusted prices, accurate as of around June 2026. If you're using this key much later, the "current" figure will be out of date — that doesn't affect the marking, since the question is a fixed, self-contained maths problem once the numbers are given.

iroriSection A · Real-World ROI

Section A · Return on Investment

Answers — Questions 1 & 2

Question 1 — The Ten-Year BetHard

Given: P = $14, current value = $200, t = 10 years

(a) ROI% = (Return − P) / P × 100 = (200 − 14) / 14 × 100 = 186 / 14 × 100

(a) ROI% ≈ 1,328.57%

(b) MV = P(1 + r/n)^(nt), with r = 0.03, n = 1, t = 10 = 14 × (1.03)^10 = 14 × 1.34392

(b) MV ≈ $18.81

(c) Model answer: the stock path turned $14 into about $200 (an extraordinary, historically unusual outcome), while the guaranteed savings path only reached about $18.81. The stock's far higher return came with far higher uncertainty — NVIDIA could just as easily have lost most of its value over those 10 years instead. Accept any answer that correctly links higher potential return to higher risk/uncertainty, using both figures.

Watch for: students dividing by 200 instead of 14 in part (a); using simple interest (I=Prt) instead of compound interest in part (b); forgetting part (c) is graded on reasoning, not a "correct" stock pick.

Question 2 — The Dream Beach HouseMedium

Given: P = RM450,000, rent = RM2,500/month × 48 months, sale price = RM520,000

Rental income = 2,500 × 48 = RM120,000 Capital gain = 520,000 − 450,000 = RM70,000 Total return = 120,000 + 70,000 = RM190,000 ROI% = 190,000 / 450,000 × 100

ROI% ≈ 42.22%

Watch for: students using 4 (years) instead of 48 (months) when calculating total rental income; students forgetting to include rental income at all and only computing capital gain.

iroriSection A · Real-World ROI (cont.)

Question 3 — Maya's Birthday MoneyMedium

Given: 800 units @ RM5 = RM4,000; 2 dividends of 15 sen/unit; sold at RM7.50/unit

Dividends = 2 × 0.15 × 800 = RM240 Sale value = 800 × 7.50 = RM6,000 Capital gain = 6,000 − 4,000 = RM2,000 Total return = 240 + 2,000 = RM2,240 ROI% = 2,240 / 4,000 × 100

ROI% = 56%

Watch for: students using only 1 dividend payment instead of 2; students computing dividend as a percentage instead of sen-per-unit × units.

Question 4 — Iskandar's Steady HabitMedium

Given: RM500/month for 6 months at unit prices RM2.00, 2.20, 1.80, 2.10, 1.90, 2.40

Units bought each month = 500 ÷ price: 250 + 227.27 + 277.78 + 238.10 + 263.16 + 208.33 ≈ 1,464.64 units Total invested = 500 × 6 = RM3,000 Average cost/unit = 3,000 / 1,464.64

(a) Average cost ≈ RM2.05 per unit

(b) Model answer: because the same RM500 buys more units when the price is low and fewer units when the price is high, the average cost automatically gets pulled down compared to a simple average of the six prices — the strategy removes the pressure to predict the "right" time to invest.

Watch for — this is the most commonly miscalculated question in the set: students taking a simple average of the 6 prices (2.00+2.20+1.80+2.10+1.90+2.40)/6 = RM2.07, instead of total invested ÷ total units. The two numbers are close but conceptually different — the simple average ignores that more units get bought when prices are low, which is the entire point of the strategy. Award full marks only for the correct units-based method, even if the final number is close.

Quick comparison (Q1–4): highest ROI% is Question 1 (≈1,329%), but also by far the highest risk and the least liquid in the sense that it depends entirely on one company's fortunes. Question 2 (the house) has solid ROI but ties up the most capital and is the least liquid to exit quickly. Questions 3 and 4 are the most balanced for a smaller investor. Accept any answer that correctly orders the ROI% and gives a sound risk/liquidity reason for the final choice.

iroriSection B · Compound Interest

Section B · Compound Interest

Answers — Questions 5 to 8

Question 5 — University FundMedium

P = RM15,000, r = 3.5%, n = 4 (quarterly), t = 4 years

MV = 15,000 × (1 + 0.035/4)^(4×4) = 15,000 × (1.00875)^16

MV ≈ RM17,243.60

Watch for: using the exponent "4" alone instead of nt = 16; forgetting to divide r by n inside the brackets.

Question 6 — Same Deal, Compounded DifferentlyMedium

Same P, r, t as Q5, but n = 12 (monthly)

MV = 15,000 × (1 + 0.035/12)^(12×4) ≈ RM17,250.59 Difference = 17,250.59 − 17,243.60

MV (monthly) ≈ RM17,250.59 — about RM6.99 more than quarterly

Watch for: students expecting a large difference — the actual gap is small, which is itself worth discussing: compounding frequency matters more at higher rates or over longer periods.

Question 7 — Compound vs Simple, Head to HeadMedium

Same P = 15,000, r = 3.5%, t = 4, compared against Q5's compound result

Simple interest: I = 15,000 × 0.035 × 4 = RM2,100 Compound interest earned (quarterly, from Q5): 17,243.60 − 15,000 = RM2,243.60 Extra from compounding = 2,243.60 − 2,100 = RM143.60 As % of simple interest = 143.60 / 2,100 × 100

Extra ≈ RM143.60, which is about 6.84% more than the simple-interest amount

Watch for: students reporting only the RM amount and skipping the percentage part of the question.

Question 8 — Working Backward for a CarHard

Target MV = RM20,000, r = 4%, n = 1, t = 5 — solve for P

MV = P(1 + r/n)^(nt) → P = MV / (1 + r/n)^(nt) P = 20,000 / (1.04)^5

P ≈ RM16,438.54

Watch for: students multiplying instead of dividing when rearranging; students re-solving for MV instead of P.

iroriSection C · Simple Interest

Section C · Simple Interest

Answers — Questions 9 to 12

Question 9 — Months, Not Just YearsMedium

P = RM6,000, r = 2.8%, t = 3 years 6 months = 3.5 years

I = 6,000 × 0.028 × 3.5

I = RM588.00

Watch for: students using t = 3 and forgetting to convert the extra 6 months to 0.5.

Question 10 — Two Banks, One DecisionMedium

P = RM5,000, t = 2 years. Bank Cahaya: 3% simple, no bonus. Bank Mentari: 2.5% simple + RM150 bonus.

Cahaya: I = 5,000 × 0.03 × 2 = RM300 → total = RM5,300 Mentari: I = 5,000 × 0.025 × 2 = RM250 → total = 5,000 + 250 + 150 = RM5,400

Bank Mentari gives more in total (RM5,400 vs RM5,300), despite the lower rate, because of the sign-up bonus.

Watch for: students comparing only the interest amounts and forgetting to add the RM150 bonus before comparing totals.

Question 11 — Paying Back a FriendMedium

P = RM3,500, r = 4%, t = 9 months = 0.75 years

I = 3,500 × 0.04 × 0.75 = RM105 Total owed = 3,500 + 105

Total owed = RM3,605.00

Watch for: students forgetting to convert 9 months to 0.75 years; students reporting only the interest (RM105) instead of the total owed.

Question 12 — Finding the Hidden RateHard

P = RM8,000, t = 5 years, I = RM1,800 — solve for r

I = P × r × t → r = I / (P × t) r = 1,800 / (8,000 × 5) = 1,800 / 40,000 = 0.045

r = 4.5% per year

Watch for: students leaving the answer as a decimal (0.045) instead of converting to a percentage.