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Something to get you started... Learning Intention: Evaluate the concept of compound interest and how it impacts the world around us. Take out your books and open them on your homework page. We are going to go through the answers together RED: A bank is offering 2.5% simple interest on a savings account. If you deposit $5000, how much interest will you earn in one year? AMBER: Bertha deposited $1000 into a retirement account when she was 18. How much will Bertha have in this account after 50 years at a yearly simple interest rate of 7.5%? GREEN: Robert deposits $ 3000 in State Bank of India for 3 years which earn him an interest of 8%. What is the amount he gets after... a) 1 year b) 2 years c) 3 years? EXTENSION: Nancy invested $6000 in a bond at a yearly rate of 3%. She earned $450 in interest. How long was the money invested? CHALLENGE: Mr. Mogi borrowed $9000 for 10 years to make home improvements. If he repaid a total of $20,000 at what interest rate did he borrow the money? Sep 1207:03 Something to get you started... Answers: Learning Intention: Evaluate the concept of compound interest and how it impacts the world around us. Visualiser: Comparing different ways of setting out our calculations. Sep 1207:03 Number: Percentage application Evaluate the concept of compound interest and how it impacts the world around us. Now that I can find my multiplier.... ...how can I use it? Develop an Illustrate Compare the the process difference of calculating between simple simple and compound around the interest. interest. world. Jun 3015:41 understanding of how compound interest is used Learning Intention: Evaluate the concept of compound interest and how it impacts the world around us. Based on the discussion so far today, write down something new that you have learnt about dealing with percentages. Oct 2420:46 Learning Intention: Evaluate the concept of compound interest and how it impacts the world around us. Simple Interest is mostly used as a simplified model to help students and adults understand the principle of calculating interest. The standard formula(e) for calculating the interest is/are A = P(1 + rt) or A = P(1 + Rt) 100 A = Total Accrued amount (principal + interest) P = Principal amount r = Rate of interest as a decimal R = Rate of interest as a percentage (which we then divide by 100 to turn it into a decimal) t = Time period involved in months or years. Imagine you wanted to borrow $20,000 to buy a new kitchen. The $20,000 is the amount you will be borrowing, the principal. The bank offers you a rate of 6% interest on the loan, this is our rate of interest, R. We can turn it into a decimal by dividing by 100. r= 6 = 0.06 100 You agree to pay the bank back the $20,000 plus the interest over 5 years or 60 months. This is the time period, t. So, the total amount you would expect to pay the bank back is called the Total Accrued amount, A. Using our formula. A = P (1 + rt) Substituting in our numbers. A = 20000(1 + 0.06 x 5) = 20000 x 1.3 = $26000 Once we have paid the bank back, they will be $6000 dollars better off Jun 3015:41 Learning Intention: Evaluate the concept of compound interest and how it impacts the world around us. Compound Interest is a more realistic model, and takes into account the fact that the amount you are paying off, or the amount that you are being paid interest on, changes over time. The standard formula for calculating the compound interest is: A = P(1 + r nt ) n A = Future value of the investment/loan (principal + interest) P = Principal amount (the initial deposit or loan amount) r = Rate of interest as a decimal t = Time period involved in months or years. n = the number of times that interest is compounded per year. Let us look to borrowing the same $20,000 to buy a new kitchen. The $20,000 is the amount you will be borrowing, the principal. The bank offers you a rate of 6% interest on the loan, this is our rate of interest as a percentage. As a decimal we would have 0.05. We agree to pay back the loan over a period of 5 years, or 60 months, this is our time period. Our loan, however, is compounded monthly. So, the total amount you would expect to pay the bank back is called the Total Accrued amount, A. Using our formula. A = P(1 + r nt ) n Substituting in our numbers. A = 20000(1 + 0.06) 12x5 12 = 20000 x (1.005) (total number of months in 5 years) (12 months in a year) 60 = 26,977.003050986321.... = $26,977.00 (The Dollar has 2 decimal places) Once we have paid the bank back, they will be $6977 dollars better off. Jun 3015:41 Learning Intention: Evaluate the concept of compound interest and how it impacts the world around us. Simple Interest: Imagine that you are calculating a simple interest of 5% on savings of $1000 over a period of 5 years. At the end of the first year: Savings = 1000(1 + 0.05) = 1050 At the end of the second year : Savings = 1000(1 + 0.05x2) = 1100 At the end of the third year: Savings = 1000(1 + 0.05x3) = 1150 At the end of the fourth year : Savings = 1000(1 + 0.05x4) = 1200 At the end of the fifth year: Savings = 1000(1 + 0.05x5) = 1250 So, for Simple interest, we are adding 5% of the original amount each time. ie 1000 ( 1 + 0.05 + 0.05 + 0.05 + 0.05 + ....) A = P(1 + r x t) A = P(1 + rt) Jun 3015:41 Learning Intention: Evaluate the concept of compound interest and how it impacts the world around us. Compound Interest: Imagine that you are calculating compound interest of 5% per year on savings of $1000 over a period of 5 years. At the end of the first year: Savings = 1000(1 + 0.05) = 1050 At the end of the second year : 2 Savings = 1000(1 + 0.05) = 1102.50 At the end of the third year: 3 Savings = 1000(1 + 0.05) = 1157.625 = 1157.63 At the end of the fourth year : 4 Savings = 1000(1 + 0.05) = 1215.50625 = 1215.51 At the end of the fifth year: 5 Savings = 1000(1 + 0.05) = 1276.2815625 = 1276.28 So, for Compound Interest with a yearly rate, we are adding 5% of the previous value each time. ie 1000( 1 + 0.05) x ( 1 + 0.05) x ( 1 + 0.05) x ..... A = P x (1 + r) A = P(1 + r) t t In the real world, compound interest is calculated multiple times during year. Sometimes 4 times a year, but mostly 12 (ie every month). So, we modify the formula. We split the yearly rate of compound interest equally between the number of installments that will be paid. This means that over the course of the repayment, interest will be added 5 x number of installments. Hence, the formula: A = P(1 + r n nt ) Jun 3015:41