CSEC MATHEMATICS · MODULE 1 · LESSON A6

Interest, Hire Purchase, Appreciation and Depreciation

Simple and compound interest, hire purchase and mortgages, the cost of borrowing, and the growth or decay of value over time.

Fundamentals of Secondary Level MathematicsM1 2.5M1 2.6M1 2.7M1 2.8≈ 40 min🎮 3 games
Before you start

By the end of this lesson you can…

Step 1 · Watch

Explainer video

5 narrated scenes. Press play, listen and read along — the points appear as they are explained. Use ‹ Prev / Next › or the scene bar to jump to any scene.

LESSON A6 · EXPLAINER

Interest, Hire Purchase, Appreciation and Depreciation

Borrow $15 000 and repay $18 000 — is that a good deal? This lesson gives you the tools to decide, and to answer the money questions in Paper 02.

Narration uses your device’s built-in voice. No sound? Switch to “Captions only” — the captions advance on their own.

Explore in 3D

Simple and compound interest

Compare the two for different amounts, rates and times.

Step 2 · Read

Key notes

Copy these into your notebook in your own words — that is how they stick.

Simple interest

I = PRT/100; A = P + I. T is in years (months ÷ 12).

Compound interest

A = P(1 + r/100)ⁿ; C.I. = A − P. Half-yearly: r/2, 2n periods; quarterly: r/4, 4n.

Hire purchase

HP price = deposit + instalments; cost of credit = HP − cash price; interest as % of cash/principal.

Loans / mortgages

Total repaid = payment × number of payments; interest = total repaid − loan.

Reducing balance

V = V₀(1 − r/100)ⁿ for depreciation, V₀(1 + r/100)ⁿ for appreciation.

Straight-line

Constant loss each year: V = V₀ − (r% of V₀) × n.

Compare

Compound interest > simple interest for the same P, R, T when T > 1.

Units

Rate and time must match: per annum with years, per month with months.

EXAM TIPS & COMMON MISTAKES

  • Convert months to years for simple interest: 18 months = 1.5 years.
  • Compound interest answer = A − P. Some students stop at A, which is the AMOUNT, not the interest.
  • Write the formula, substitute, then evaluate — the substitution line usually earns the method mark.
  • For “percentage interest on a loan”, divide the interest by the PRINCIPAL (amount borrowed) unless told otherwise.
Play & practise

Games

3 quick games on this lesson. Earn XP and badges as you play — your best score for each game is saved. Games are for practice and do not change your exam readiness. More games in the Mathematics Arcade.

Step 3 · Practise

Paper 1 practice — multiple choice

8 items modelled on real CSEC Paper 1 questions. Choose one answer for each, then check. Aim for 80% or better. Work each item on paper first.

CSEC Paper 01 style · SO 2.6

1. Simple interest on $5 000 at 6% per annum for 3 years is

Answer: A. I = 5 000 × 6 × 3 ÷ 100 = $900.
Adapted from CSEC P1 May/June 2024 (hire purchase item)

2. A television set costs $350 cash. When bought on hire purchase, a deposit of $35 is required, followed by 12 monthly payments of $30 each. How much money is saved by paying cash?

Answer: B. HP price = 35 + 360 = $395; 395 − 350 = $45.
Adapted from CSEC P1 May/June 2024 (loan item)

3. A loan of $15 000 was repaid in 24 equal monthly instalments of $750. The total interest paid as a percentage of the principal was

Answer: C. Repaid 24 × 750 = 18 000; interest 3 000; 3 000/15 000 × 100 = 20%.
CSEC Paper 01 style · SO 2.7

4. $2 000 is invested at 5% per annum compound interest. After 2 years the amount is

Answer: D. 2 000 × 1.05² = 2 000 × 1.1025 = $2 205.
CSEC Paper 01 style · SO 2.6

5. The principal that earns simple interest of $240 in 2 years at 6% per annum is

Answer: A. P = 100 × 240 ÷ (6 × 2) = $2 000.
CSEC Paper 01 style · SO 2.8

6. A car valued at $80 000 depreciates by 10% of its value each year (reducing balance). Its value after 2 years is

Answer: B. 80 000 × 0.9² = 80 000 × 0.81 = $64 800.
CSEC Paper 01 style · SO 2.7

7. Which statement about $1 000 invested for 3 years at 5% per annum is TRUE?

Answer: C. Simple: $150. Compound: 1 000 × 1.05³ − 1 000 = $157.63.
CSEC Paper 01 style · SO 2.5

8. Mr Lee borrowed $200 000 for a house and repaid $1 500 per month for 20 years. The interest he paid was

Answer: D. Total repaid 1 500 × 240 = $360 000; interest = 360 000 − 200 000 = $160 000.
Step 4 · Apply

Paper 2 practice — structured questions

Write full answers, then reveal the mark scheme and tick the points you earned (18 marks in total). Show all your working — method marks count. Your answers are saved on this device.

CSEC Paper 02 style · Module 1 (Interest)

Question 1 [9 marks]

Mr Brown invests $8 000 at 4% per annum.

(a) Calculate the simple interest earned in 3 years. [2]

MARK SCHEME — (a) (max 2)

(b) The same money is invested at 4% per annum compound interest for 3 years. Calculate (i) the amount, (ii) the compound interest, correct to the nearest cent. [4]

MARK SCHEME — (b) (max 4)

(c) Find the difference between the two kinds of interest. [1]

MARK SCHEME — (c) (max 1)

(d) State TWO reasons why compound interest is greater than simple interest. [2]

MARK SCHEME — (d) (max 2)

CSEC Paper 02 style · Module 1 (Hire purchase and depreciation)

Question 2 [9 marks]

A sofa has a cash price of $2 400. It may be bought on hire purchase with a deposit of 20% of the cash price followed by 18 monthly payments of $135.

(a) Calculate the deposit. [1]

MARK SCHEME — (a) (max 1)

(b) Calculate the total hire purchase price. [2]

MARK SCHEME — (b) (max 2)

(c) How much more is paid by hire purchase, and what is this as a percentage of the cash price? [3]

MARK SCHEME — (c) (max 3)

(d) If the sofa loses 12% of its value each year (reducing balance), find its value after 2 years. [3]

MARK SCHEME — (d) (max 3)

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Sources

Where this topic appears in CSEC papers

Find these in your own past-paper booklets for extra timed practice. Items above are written in the style of these papers; any adapted from a specific question say so.