Simple & Compound Interest

Simple & Compound Interest Objective: 7.1.01 Develop and use ratios, proportions, and percents to solve problems Essential Question: How can I use percents to calculate simple and compound interest?

Simple & Compound Interest Vocabulary: Interest: an specified amount of money paid or earned for the use of money. Principal: the original amount of money borrowed or deposited. Rate: the interest percentage. Time: the period of time for which an amount of money is invested or borrowed. Simple Interest: an interest calculation that is calculated only on the principal. Compound Interest: an interest calculation that is calculated using the principal and any interest remaining in an account.

Real World Example: Simple & Compound Interest I = Prt Simon is 12 years old and has decided that he wants to buy a car when he turns 16. He has some money and thinks if he puts it in the bank for the next four years he will get enough interest to buy a car. If he invests $3000 and receives 4% simple interest over the next four years, how much will he have to spend on a new car? I = Prt I = (3000)(0.04)(4) I = $480 Simon will have a total of $3,480 to spend on a car when he turns 16

Simple & Compound Interest Simple Interest Formula I = Prt Time (in years) Interest Rate Principal

Simple & Compound Interest Compound Interest Formula B = P(1 + )nt r n Time (in years) Balance Rate Principal

Simple & Compound Interest Example 1: Finding Simple Interest Find the simple interest for $4,000 invested for 4 years at an annual interest rate of 4%. I = Prt I = ? I = (4000)(0.04)(4) P = 4,000 I = $640 r = 4% = 0.04 $4,000 + $640 t = 4 years $4,640.00

Simple & Compound Interest Example 2: Finding Compound Interest If you deposit $4,000 in an account that pays 4% compounded annually what is your balance after 4 years. B = p(1 + r)t B = ? B = 4000(1 + 0.04)4 p = 4,000 B = $4679.43 r = 4% = 0.04 t = 4 years $4,679.43

Simple & Compound Interest Example 3: Finding Simple Interest Find the simple interest for $2,500 invested for 4½ years at an interest rate of 4.5%. I = Prt I = ? I = (2500)(0.045)(4.5) P = 2,500 I = $506.25 r = 4.5% = 0.045 $2,500 + $506.25 t = 4.5 $3,006.25

Simple & Compound Interest Example 4: Finding Simple Interest Find the simple interest for $80 invested for 6 months earning 6% simple interest. I = Prt I = ? I = (80)(0.06)(6/12) P = 80 I = $2.40 r = 6% = 0.06 $80.00 + $2.40 t = 6/12 = 0.5 $82.40

Simple & Compound Interest Example 5: Using Simple Interest to Find Time If you invest $8,000 and receive 9% simple interest, how long would it take to earn $5,040 in interest. I = Prt I = 5,040 5040 = (8000)(0.09)(t) P = 8,000 5040 = 720t r = 9% = 0.09 720 720 t = ? t = 7 years

Simple & Compound Interest Example 6: Using Simple Interest to Find Rate If you invest $8,000 and receive $5040 in simple interest after 7 years, what was the interest rate. I = Prt I = 5,040 5040 = (8000)(r)(7) P = 8,000 5040 = 56000r r = ? 56000 56000 t = 7 r = 0.09

Simple & Compound Interest When Calculating Interest: Always Remember… First make sure you are using the correct formula…is it simple interest or compound interest? Make the correct substitutions…p is principal, r is interest rate, t is time in years, and B is balance. Solve for the unknown. Reread the question and calculate your answer.

Simple & Compound Interest Independent Practice: Find the interest for each example below: 1. $800, 5 years, 5% interest 2. $1,500, 6½ years, 8% interest 3. $450, 7 years, 11.75% interest = $200.00 = $780.00 = $370.13

Simple & Compound Interest Independent Practice: Find the interest for each example below: 1. $800, 5 years, 5% interest 2. $1,500, 6½ years, 8% interest 3. $450, 7 years, 11.75% interest = $200.00 = $780.00 = $370.13

Simple & Compound Interest HOMEWORK