Year 10 Maths Revision: Simple Interest Video Walkthrough

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Let's explore simple interest fundamentals. Simple interest is calculated using the formula I equals P times R times T, where I is interest, P is principal, R is the annual rate as a decimal, and T is time in years. For question 1, we have 800 dollars at 7 percent for 5 years. Converting 7 percent to decimal gives 0.07. So interest equals 800 times 0.07 times 5, which equals 280 dollars. For question 2, we find the total repayment. With principal 2000 dollars at 10 percent for 4 years, interest equals 2000 times 0.10 times 4, giving 800 dollars interest. The total repayment is principal plus interest, so 2000 plus 800 equals 2800 dollars. Now let's explore simple interest applications by rearranging the formula to solve for different variables. We can rearrange I equals P times R times T to find time as T equals I divided by P times R, or rate as R equals I divided by P times T. For question 3, we have 1500 dollars earning 225 dollars interest at 5 percent per annum. We need to find the time. Using T equals I over P times R, we get T equals 225 divided by 1500 times 0.05, which equals 225 divided by 75, giving us 3 years. Question 4 asks for interest on 1200 dollars at 3.5 percent for 2 and a half years. Using our original formula, I equals 1200 times 0.035 times 2.5, which equals 105 dollars. The challenge question involves a 5000 dollar loan at 6 percent with 1800 dollars interest paid. Using T equals I over P times R, we get T equals 1800 divided by 5000 times 0.06, which equals 1800 divided by 300, giving us 6 years. Now let's explore compound interest, where interest earns interest. The compound interest formula is A equals P times 1 plus r to the power n, where A is the final amount, P is principal, r is the rate per period, and n is the number of periods. Unlike simple interest, compound interest grows exponentially because each period's interest is added to the principal for the next calculation. For question 5, we have 1000 dollars at 8 percent for 2 years. Using the formula, A equals 1000 times 1.08 squared, which equals 1000 times 1.1664, giving us 1166 dollars and 40 cents. The compound interest is 166 dollars and 40 cents, which is 6 dollars and 40 cents more than simple interest would give. For question 6, 5000 dollars at 5 percent for 3 years gives us A equals 5000 times 1.05 cubed, which equals 5000 times 1.157625, resulting in 5788 dollars and 13 cents. Advanced compound interest problems often require solving for unknown rates using algebraic manipulation and logarithms. When we know the final amount, principal, and time, we can rearrange the compound interest formula. For question 7, 2000 dollars grows to 2197 dollars in 2 years. We set up the equation 2197 equals 2000 times 1 plus r squared. Dividing both sides by 2000 gives us 1 plus r squared equals 1.0985. Taking the square root gives us 1 plus r equals 1.048, so r equals 0.048 or 4.8 percent. Question 8 is straightforward: 1500 dollars at 3 percent for 4 years gives us A equals 1500 times 1.03 to the fourth power, which equals 1688 dollars and 25 cents. The challenge question has 2500 dollars becoming 2960 dollars in 3 years. Setting up 2960 equals 2500 times 1 plus r cubed, we get 1 plus r cubed equals 1.184. Taking the cube root gives us 1 plus r equals 1.0579, so r equals 5.79 percent to two decimal places. Exponential growth models apply the compound interest formula to various real-world scenarios. The general formula is A equals P times 1 plus r to the power t, where the growth factor is 1 plus the rate. For question 9, a population of 2000 grows at 5 percent per year. After 10 years, the population equals 2000 times 1.05 to the tenth power, which equals 2000 times 1.6289, giving us 3258 people. For doubling problems like question 11, we use A equals P times 2 to the power n, where n is the number of doubling periods. With 500 bacteria doubling every 3 hours, after 9 hours we have 3 doubling periods. So the final amount is 500 times 2 cubed, which equals 500 times 8, giving us 4000 bacteria. The key insight is recognizing whether we have a percentage growth rate or a doubling time scenario.