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Lesson 8.2.4 Simple Interest

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2 Lesson 1.1.1 California Standards: Number Sense 1.3 Convert fractions to decimals and percents and use these representations in estimations, computations, and applications. Number Sense 1.6 Calculate the percentage of increases and decreases of a quantity. Number Sense 1.7 Solve problems that involve discounts, markups, commissions, and profit and compute simple and compound interest. What it means for you: Youll see what interest is and how to work out how much simple interest you could earn over time. Lesson 8.2.4 Key words: interest simple interest principle interest rate Simple Interest

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3 Lesson 1.1.1 Interest is an important real-life topic because its all about saving and borrowing money. Lesson 8.2.4 If you keep your money in a savings account, the bank will pay you something just for keeping it there. The interest that you gain will be based on how much you put in and that means its another use of percent increase. Simple Interest

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4 Lesson 1.1.1 Interest is a Fee Paid For the Use of Money Lesson 8.2.4 When you keep money in a savings account, the bank pays you interest for the privilege of using your money. When you borrow money from a bank, the bank charges you interest for the privilege of using their money. Interest is a fee that you pay for using someone elses money. The interest to be paid is worked out as a percent of the money invested or loaned. The percent that is paid over a given time is called the interest rate. Simple Interest

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5 Lesson 1.1.1 Simple Interest is Paid Only on the Principal Lesson 8.2.4 The amount of money you put into or borrow from a bank is called the principal. With simple interest, the interest rate tells you how much money you will get back every year as a percent of the principal. Interest that is paid only on the principal is called simple interest. Simple Interest

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6 For example: think about depositing $100 in a savings account with a simple interest rate of 5% per year. Lesson 1.1.1 Lesson 8.2.4 For each year you leave your money in the account, you will get 5% of $100 back. Simple Interest

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7 Example 1 Lesson 8.2.4 You deposit $50 in a savings account that pays a simple interest rate of 2% per year. How much interest will you get over 3 years? How much will be in the account after 3 years? Solution Solution follows… After 3 years you will have: First find 2% of $50: $50 × = $1. So over 3 years you will earn: 3 × $1 = $3 This is the amount of interest you will get each year. 2 100 $50 + (3 × $1) = $53 in the account. Simple Interest

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8 1. If you put money into a savings account which pays simple interest, will the amount of interest you get in the first year be the same as in the second year? Explain your answer. 2. You borrow $150 from a bank at a simple interest rate of 8% per year. How much interest will you pay in one year? Lesson 1.1.1 Guided Practice Lesson 8.2.4 Solution follows… Yes. Simple interest is calculated as a percent of the principle, so you receive the same amount of interest each year. 150 × (8 ÷ 100) = $12 Simple Interest

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9 3. You deposit $200 in a savings account that pays a simple interest rate of 5% per year. How much interest will you get over 4 years? 4. You deposit $65 in a savings account that pays a simple interest rate of 4% per year. How much will be in your account after 4 years? Lesson 1.1.1 Guided Practice Lesson 8.2.4 Solution follows… 200 × (5 ÷ 100) = 10 10 × 4 = $40 65 × (4 ÷ 100) = 2.6 2.6 × 4 = 10.4 65 + 10.4 = $75.40 Simple Interest

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10 Lesson 1.1.1 Use the Simple Interest Formula to Calculate Interest Lesson 8.2.4 In Example 1, to work out how much interest you got over 3 years, you worked out the percent of the principal that you would get each year and multiplied it by 3. So the calculation you did was: 2 100 (50 × ) × 3 = $3 Now think about what each part of that equation represents. This is the principle. This is the interest rate written as a fraction. This is the time that the money is in the account for. This is the interest earned. You can use this to figure out a general formula for finding simple interest. Simple Interest

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11 P stands for the principal. Lesson 1.1.1 Lesson 8.2.4 To find the amount of interest ( I ) that you got, you multiplied together the principal ( P ), the interest rate ( r ), and the time ( t ) the money was in the account for. First assign a variable to stand for each part of the equation: Written as a formula this is: I = Prt r stands for the interest rate (in % per year), written as a fraction or a decimal. I stands for the amount of interest that has built up. t stands for time (in years). Simple Interest

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12 Example 2 Lesson 8.2.4 You deposit $276 in a savings account that has a simple interest rate of 6% per year. How much interest will you get over 5 years? Solution Solution follows… I = $82.80 I = Prt I = $276 × 0.06 × 5 Over 5 years youll earn $82.80 interest. Substitute the values Write out the formula Do the multiplications Simple Interest

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13 5. You borrow $57 from a bank at a simple interest rate of 9% per year. How much interest will you pay in one year? 6. You deposit $354 in a savings account that pays a simple interest rate of 2.5% a year. How much interest will you get over 7 years? 7. You deposit $190 in a savings account that pays a simple interest rate of 4% a year. How much will be in your account after 4 years? 8. You put $520 in a savings account with a simple interest rate of 6% a year. You take it out after 6 months. How much interest will you get? Lesson 1.1.1 Guided Practice Lesson 8.2.4 Solution follows… I = Prt = 57 × 0.09 × 1 = $5.13 I = Prt = 354 × 0.025 × 7 = $61.95 I = Prt = 190 × 0.04 × 4 = 30.40, and 190 + 30.40 = $220.40 I = Prt = 520 × 0.06 × 0.5 = $15.60 Simple Interest

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14 1. You borrow $75 from a bank at a simple rate of 9% per year. How much interest will you pay over 7 years? 2. You deposit $64 in a savings account that pays a simple interest rate of 2.5% a year. How much will be in your account after 17 years? 3. Ian put $4000 into a short-term investment for 3 months. The simple interest rate was 5.2% per year. How much interest did Ian earn? 4. Luz borrows money from a bank at a simple interest rate of 5% a year. After 4 years she has paid $50 interest. How much did she borrow? Independent Practice Solution follows… Lesson 8.2.4 $52 $47.25 $91.20 $250 Simple Interest

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15 6. Anna puts $50 in a savings account that pays a simple interest rate of 5% a year. After 4 years she takes out all the money, and puts it in a new account that pays a simple interest rate of 6% a year. She leaves it there for 5 years. How much will Anna have in total at the end of this time? Independent Practice Solution follows… Lesson 8.2.4 Ty has used 3 instead of 0.03 to represent 3% in his calculation. The correct calculation is: $50 × 0.03 × 5 = $7.50 $78 5. Ty puts $50 in a savings account with a simple interest rate of 3% a year. He works out what interest he will get in 5 years. His calculation is shown on the right. What error has he made? How much interest will he get? Simple Interest

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16 Lesson 8.2.4 Round Up Simple Interest Interest is money that is paid as a fee for using someone elses money. Simple interest means that each year you get back a fixed percent of the initial amount you invested. Make sure you understand how simple interest works. Youll use a lot of the same math in the next lesson on compound interest.

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