Last reviewed: 7 November 2026
Updated November 2026. These Grade 8 notes on appreciation, depreciation and hire purchase show how values grow or fall by a percentage each year, worked step by step for up to three years, and how to find the total cost of buying on hire purchase. Hire purchase price = deposit + (number of instalments × instalment).
All prices and rates below are made-up practice figures. For simple and compound interest, see our Grade 8 simple and compound interest notes, and for other topics the Grade 8 mathematics revision guide.
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What the Grade 8 Curriculum Covers
Money is a sub-strand under Measurements in the Kenya Institute of Curriculum Development’s Grade 8 Mathematics design. It includes interest, appreciation and depreciation per annum worked step by step up to three years, and hire purchase. The design is listed on the KICD Grade Eight curriculum designs page. The idea of percentage growth is also explained in OpenStax Contemporary Mathematics.
Appreciation
Appreciation is an increase in value over time, as often happens with land. Each year the value rises by a percentage of the value at the start of that year.
Example. A plot is worth KSh 500,000 and appreciates at 10% per year.
- Year 1: 500,000 + 10% of 500,000 = 550,000
- Year 2: 550,000 + 55,000 = 605,000
- Year 3: 605,000 + 60,500 = 665,500
Total appreciation after 3 years = 665,500 − 500,000 = KSh 165,500.
Depreciation
Depreciation is a fall in value over time, as with vehicles, phones and machines. Each year the value falls by a percentage of the value at the start of that year.
Example. A motorbike bought for KSh 160,000 depreciates at 20% per year.
- Year 1: 160,000 − 32,000 = 128,000
- Year 2: 128,000 − 25,600 = 102,400
- Year 3: 102,400 − 20,480 = 81,920
Note that the drop gets smaller each year, because 20% is taken from a smaller value each time.
Hire Purchase
Hire purchase lets a buyer take goods home after paying a deposit, then pay the rest in equal instalments. The total paid is usually more than the cash price.
Example. A fridge has a cash price of KSh 36,000. On hire purchase the buyer pays a deposit of KSh 9,000 and 12 monthly instalments of KSh 2,600.
- Hire purchase price = 9,000 + 12 × 2,600 = 9,000 + 31,200 = KSh 40,200
- Extra paid = 40,200 − 36,000 = KSh 4,200
- Extra as a percentage of the cash price = 4,200/36,000 × 100 = 11.67% (to 2 decimal places)
Original Practice Questions With Worked Answers
- A house worth KSh 2,000,000 appreciates at 5% per year. Find its value after 2 years.
Answer: 2,100,000 after year 1; 2,205,000 after year 2. - A laptop worth KSh 50,000 depreciates at 10% per year. Find its value after 3 years.
Answer: 45,000; 40,500; 36,450. Value = KSh 36,450. - A TV costs KSh 30,000 cash. On hire purchase the deposit is KSh 6,000 and there are 10 instalments of KSh 2,700. Find the extra paid.
Answer: 6,000 + 27,000 = 33,000; extra = KSh 3,000. - A cooker has a hire purchase price of KSh 21,000. The deposit is KSh 5,000 and there are 8 equal instalments. Find each instalment.
Answer: (21,000 − 5,000) ÷ 8 = KSh 2,000.
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Frequently Asked Questions
What is the difference between appreciation and depreciation?
Appreciation is an increase in value over time. Depreciation is a decrease in value over time.
Why do I work depreciation year by year?
Each year’s percentage is taken from the value at the start of that year, so the amount changes every year. Grade 8 works this step by step for up to three years.
How do I find the hire purchase price?
Add the deposit to the total of all the instalments.
Why is hire purchase dearer than cash?
The seller charges extra for letting the buyer pay over time, so the total of the deposit and instalments is usually higher than the cash price.
Ten-minute check: try the free Grade 8 CBC Challenge. It has 10 questions, each marked on the spot with the working, and it shows which topics to practise next.