Grade 8Mathematics

Money

Compound interest; appreciation, depreciation; hire purchase; bills, invoices, taxes.

📖 5 min read · 3 worked examples · 8 practice questions

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The lesson

Today we're starting our session on Money within Measurements. By the end of the next 20 minutes, you'll be able to calculate interest, understand depreciation, work out hire‑purchase payments, and read bills and taxes confidently. First, let's connect money calculations to our everyday lives here in Kenya—whether it's budgeting for school supplies, saving for a family trip, or figuring out the cost of a matatu ride. Our learning objectives are clear: we'll compute simple interest, explore how depreciation reduces the value of items over time, break down hire‑purchase agreements, and interpret the numbers on utility bills and tax receipts. Lastly, here's our agenda for this short session: a quick introduction, step‑by‑step examples for each skill, and a brief Q&A to make sure everyone is comfortable with the concepts.

Class, today we're diving into the basics of compound interest – a powerful idea that helps your savings grow over time. First, what is compound interest? It's the interest you earn not only on your original amount, the principal, but also on the interest that has already been added. The formula looks like this: A equals P times (1 plus r) to the power of n. Here, P is the principal, r is the interest rate per period, n is the number of periods, and A is the amount you'll have after those periods. At this line chart. It shows how Ksh 1,000 grows at a 5% yearly rate over five years. Notice the line curves upward – that's the effect of earning interest on interest. To recap, compound interest means earning interest on both the original money and the interest already earned, and we can calculate the future amount using the formula A = P(1+r)^n. Great job following along!

Let's dive into today's topic: Appreciation and Depreciation of assets. First, appreciation means an asset's value goes up over time—think of land or livestock that become more valuable as they age or as demand grows. Conversely, depreciation is when an asset loses value, like a car or a phone that get older and wear out. A simple way to estimate these changes is the linear model: New Value equals Original value plus or minus the Rate multiplied by the number of years. Mathematically we write New Value = Original ± Rate × Years. This formula will help us calculate both appreciation and depreciation quickly.

Class, let's dive into hire‑purchase and bills. This slide covers what a hire‑purchase agreement looks like and how we read a simple bill, especially in a Kenyan context. First, hire‑purchase means you pay a down‑payment up front, then a series of equal instalments that include interest. It's like buying a bike now and paying the rest over time. The total amount you will pay is simply the down‑payment plus the sum of all instalments. We'll use this formula to calculate the final cost. You might put down KSh 10,000 and then pay the remaining KSh 40,000 in equal monthly instalments with interest. When you read a bill, you'll see three main parts: the item cost, a 16 % VAT, and any service charge. Adding them gives you the total amount due, just like our formula.

Class, we've reached the end of today's lesson. Let's review the key take‑aways so you can see how these formulas fit into everyday life in Kenya. First, compound interest: A = P (1 + r)^n. Remember, this is how savings grow over time, like the interest on a KES 10,000 deposit in a local bank. Next, depreciation and appreciation follow a linear model—useful when estimating the value change of a motorbike or a piece of farm equipment each year. Third, hire‑purchase combines a down‑payment with regular instalments plus interest. It's the same method many families use to buy a fridge or a smartphone. Finally, when you add a 16 % VAT to any taxable amount, you're applying the basic tax formula we covered—very handy when you're budgeting for school supplies or market purchases.

Worked examples

Savings Account

All right, let's walk through our first worked example: a savings account. We start with the problem: you deposit Ksh 2,000 at an annual interest rate of 6 % for three years. To find the amount after three years, we use the compound‑interest formula A = 2000 × (1 + 0.06)^3. Calculating that gives A = Ksh 2,379.31, so after three years you'd have earned Ksh 379.31 in interest. Notice how the extra earnings appear after applying the exponent three times—that's the power of compounding!

Depreciating Asset

Let's work through our second example: calculating the value of a used motorcycle after four years of depreciation. First, the original price is Ksh 120,000 and the depreciation rate is 10 % per year. We use the compound depreciation formula V = 120,000 × (1 − 0.10)^4, which means we reduce the value by ten percent each year, four times. Plugging the numbers in, (1 − 0.10) is 0.90, and 0.90 raised to the fourth power is about 0.6561. Multiplying 120,000 by 0.6561 gives us Ksh 77,760. After four years, the motorcycle is worth roughly seventy‑seven thousand seven hundred and sixty shillings. Any questions before we move on? Remember, each year we're applying the same 10 % reduction, just like how the value of a used phone drops each year.

Hire Purchase Calculation

Class, let's work through Example 3: calculating the total cost of a refrigerator using a hire‑purchase plan. First, the down‑payment is 20 % of the Ksh 60,000 price, which gives us Ksh 12,000. Subtracting that from the price leaves a financed amount of Ksh 48,000. The annual interest rate is 4 %, so the monthly rate is roughly 0.04 divided by 12. Using a simple‑interest approximation, total interest for one year equals 48,000 × 0.04 × 1 ≈ Ksh 1,920. Finally, add the down‑payment, financed amount, and interest: 12,000 + 48,000 + 1,920 = Ksh 61,920. That's the total amount you'll pay over the 12 months. By breaking the cost into a small upfront payment and manageable monthly instalments, we can see the true cost of buying on hire purchase.

Practice questions

Remember the compound‑interest formula A = P(1 + r)^n. Here P = 1,500 Ksh, r = 5% = 0.
Deals with straight‑line depreciation, which simply reduces the value by a fixed percentage each year. A 15% drop each year on a Ksh 45,000 laptop means you lose 0.
For the first question, remember the down‑payment is 25 % of the TV price, then the balance earns simple interest at 3 % per year for half a year. First, 25 % of Ksh 30,000 is Ksh 7,500, leaving a balance of Ksh 22,500.
The second question asks you to untangle VAT. The total includes a 16 % tax, so let x be the net price.
Take a moment to write down the steps you used – down‑payment, simple‑interest calculation, and solving for the net price before VAT. Those are the key take‑aways you'll need for real‑world purchases.
Remember the core formula for future value when interest is compounded annually: **FV = PV × (1 + r)^n**. That's the one you'll need for the first question, and it's the same shape you'll see in many real‑world calculators, from bank statements to mobile money apps.
For the farmer problem, think about how the balance grows each year. With compound interest, the amount added each year gets bigger because you earn interest on the interest already credited.
Finally, the profit question is just a simple revenue‑minus‑cost calculation: total profit = (selling price − cost price) × quantity. Write out the numbers, do the subtraction, then multiply by 20 books – that will give you the exact profit figure to report.

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Money

📖 The lesson

✏️ Worked examples