Today we'll look at what you'll be mastering by the end of this lesson. First, we'll understand key financial concepts—interest, appreciation, depreciation, tax, VAT, and hire‑purchase—using everyday Kenyan examples like a mobile phone loan or a farm tractor purchase. Next, we'll apply the relevant formulas to real‑world scenarios, such as calculating interest on a Ksh 10,000 loan at 12% per year. Finally, we'll solve worked examples together and give you practice problems to reinforce your skills. Keep those questions coming, and let's make these financial ideas clear and useful for you.
Class, let's dive into the concept of compound interest – a powerful idea that lets your money grow over time. Here is the standard formula: A equals P times one plus r over n, all raised to the power of n times t. This tells us the amount A you'll have after t years. Let's break down each symbol: P is the principal, the amount you start with; r is the annual interest rate; n is how many times interest is added each year; and t is the number of years you leave the money to grow. For example, if you put 1,000 Kenyan shillings in a savings account that compounds monthly at 5% per year, after 2 years you'll have about 1,104 shillings. In Kenya, many micro‑finance loans use the same principle, so understanding this formula helps you plan both savings and repayments wisely.
Let's dive into appreciation and depreciation – the two sides of how asset values change over time. First, appreciation means the value goes up, while depreciation means it goes down. We'll see how to calculate each percentage. Appreciation formula: ((New – Old) ÷ Old) × 100%. This tells us how much the asset has gained relative to its original price. Depreciation formula: ((Old – New) ÷ Old) × 100%. It measures the loss in value as a percentage of the original price. For example, a vehicle bought for 2,000,000 KES is worth 1,500,000 KES after three years. Using the depreciation formula, we get ((2,000,000 – 1,500,000) ÷ 2,000,000) × 100% = 25% loss. Appreciation and depreciation are just two ways of expressing how an asset's value moves, using the same basic percentage‑change idea.
First, let's look at the key points on the slide: the income‑tax formula, the VAT formula, and a simple example showing how you calculate net salary after tax. Income Tax is calculated by multiplying your taxable income by the applicable rate. For instance, if you earn Ksh 50,000 and the rate is 10%, your tax would be Ksh 5,000. VAT, on the other hand, is 16 % of the price before tax. If a shirt costs Ksh 1,000 before VAT, the tax added is Ksh 160, making the final price Ksh 1,160. Using these formulas, let's quickly run through an example together and see how your take‑home pay is affected after income tax is deducted.
Class, let's dive into hire‑purchase and see how it works step by step. First, the total cost of a hire‑purchase item equals the down payment plus the sum of each monthly instalment, which already includes interest. In formula terms, C = D + ∑_{i=1}^{n}(P_i + I_i). Here, C is the overall cost, D is the down payment, P_i the principal part of each instalment, and I_i the interest charged on that instalment. Notice how interest is often calculated on the reducing balance – as you pay off the principal, the interest each month gets smaller. Let's bring this home with a Kenyan example: buying a refrigerator for 30,000 KES with a 5,000 KES down payment and 12 monthly payments of 2,300 KES each. Adding everything up gives the total cost.
Let's wrap up with our key takeaways. We've covered four important financial formulas that you'll use in everyday Kenyan contexts. First, the compound interest formula: A = P(1+r/n)^{nt}. It tells us how money grows when interest is added regularly—like a savings account that compounds monthly at the Bank of Kenya rate. Next, appreciation or depreciation uses the percentage‑change formula (New – Old) / Old × 100, which helps you calculate how much a car's value has risen or fallen over time. For taxes, we apply Kenya's rates: Tax = 0.30 × Income for income tax, and similarly VAT at 0.16 × Sales. Plug those numbers in to see what you actually keep. Finally, the hire‑purchase total cost adds the down‑payment D to all scheduled instalments: Total = D + Σ_{k=1}^{m} Instalment_k. That shows the true cost of buying a laptop on credit.
