Simple Compound Interest Simple Compound Interest Objective 7

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.

Simple & Compound Interest Real World Example: 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 Interest Time (in years) Rate Principal

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

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= ? P = 4, 000 r = 4% = 0. 04 t = 4 years I = Prt I = (4000)(0. 04)(4) I = $640 $4, 000 + $640 $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. t B = p(1 + r) B= ? p = 4, 000 r = 4% = 0. 04 t = 4 years 4 B = 4000(1 + 0. 04) B = $4679. 43 $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 = (2500)(0. 045)(4. 5) I= ? 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= ? P = 80 r = 6% = 0. 06 t = 6/12 = 0. 5 I = Prt 6 I = (80)(0. 06)( /12) I = $2. 40 $80. 00 + $2. 40 $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 = 5, 040 P = 8, 000 r = 9% = 0. 09 t= ? I = Prt 5040 = (8000)(0. 09)(t) 5040 = 720 t 720 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 = 5, 040 P = 8, 000 r=? t=7 I = Prt 5040 = (8000)(r)(7) 5040 = 56000 r 56000 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 = $200. 00 2. $1, 500, 6½ years, 8% interest = $780. 00 3. $450, 7 years, 11. 75% interest = $370. 13

Simple & Compound Interest Independent Practice: Find the interest for each example below: 1. $800, 5 years, 5% interest = $200. 00 2. $1, 500, 6½ years, 8% interest = $780. 00 3. $450, 7 years, 11. 75% interest = $370. 13

Simple & Compound Interest HOMEWORK