Warmup 4-25 List transformations and analyze the following exponential function: Transformations: Domain: Range: Asymptote: Growth or Decay: 2. Simplify: Simplify: Simplify : 7. Solve for x:

Compound Interest Formula A = P(1+(r/n))nt A = Amount earned P = Principle(amount Put in) r = interest rate n = number of times compounded PER YEAR t = time in YEARS To enter compound interest in calculator, type: P((1 + (r%/n))(n*t) , enter (If calculator has no % button, divide r by100,put this decimal in for r in formula)

Notes – Compound Interest EXAMPLES Ex: John wants to invest $2000 at 4.25% for 3 years. How much would John end up with at the end of the 3 years if the interest was compounded monthly? Ex: What if the interest in the example above were compounded quarterly? How much would John have at the end of the 3 years? Ex Just before he decides on which investment to make, John finds a different offer. He can only get 4%, but the interest is compounded daily. How much would John have at the end of 3 years with this option? Ex: Meg wants to invest $18500 at 5.375% for 5 years. How much would Meg end up with at the end of the 5 years if the interest was compounded: a. Annually? b. Weekly? c. Semi-Annually? d. Daily?

Exponential Word Problems Practice For the following problems, use the formula: A = P 1 + r nt or A = Pert n If Jon has $8500 to invest for 5 years and the bank will offer a CD at 3.25%, how much would he have if the money were compounded: 1. Annually? 2. Daily? 3. Weekly? Monthly? Semi-Annually? Nicole has saved up $9600 towards going to college. She wants to invest it in an account that yields 4.5% interest for 4 years. How much money will she have at the end of the 4 years if the interest in compounded: 6. Weekly? 7. Daily? 8. Monthly? 9. Annually? Quarterly? Nick has been given $5400 to invest towards buying his first car. The bank offers an account that yields 3.75% interest for 3 years. How much money will Nick earn if the interest is compounded: 11. Quarterly? 12. Monthly? 13. Daily? Weekly?

Ticket out the Door 4-22 Compound Interest If Pam has $3500 to invest for 5 years and the bank will offer a CD at 2.75%, how much would she have if the money were compounded: Weekly? Quarterly? Semi-Annually? Monthly? Daily?

Compound Interest Part 2 (CONTINUOUSLY COMPOUNDED INTEREST) New Formula: A = Pert A = Amount Earned P = Principle(amount INVESTED) r = Interest rate t = time in years To enter this formula into calculator: P, 2nd ln(for e),(r*t) IMPORTANT: If the word “invests”is in problem,use normal formula. If the word “needs” is in problem, use the formula, P = A ert

Notes – Compound Interest Formula Pert EXAMPLES Ex. Suppose a person had $3600 to invest at 3.5% for 6 years. How much would they have at the end of the 6 years if the interest were compounded continuously? Ex. Mary won $7500 in a lottery game. She wants to invest it in an account that earns 5.75% for 4 years. If the interest is compounded continuously, how much would Mary have in the account after 4 years? Ex. Jamie has inherited $9000 from her grandparents. She wants to invest the money in an account earning 3.125% interest for 4 years. If the interest is compounded continuously, how much money will Jamie have in the account after 4 years? Pert formula part 2 Examples Ex. Janice needs to earn $10000 in 8 years from her investments. How much money would she need to invest to make this much at 4.25% interest? (interest is compounded continuously) Ex. How much would Janice need to invest in the account above if she could wait 12 years? Ex. Jack needs to earn $4800 to put towards the purchase of a car. If he can get an account that earns 5.5% interest compounded continuously, how much does he need to invest for: 4 years? 7years? 10 years?

Exponential Word Problem Practice Part 2 1. Tim has $4500 to invest. He can get an account that earns 4.75% interest compounded continuously for 5 years. How much money will be in his account at the end of the 5 years? 2. Terri has $9400 to invest. She can get an account that earns 3.5% interest compounded continuously for 3 years. How much money will be in her account after 3 years? Steve won $15000 in the lottery. He wants to invest it in an account that earns 2.875% interest for 6 years. If the interest is compounded continuously, how much money will he have after 6 years? Amanda won $3200 in a radio contest. She wants to invest the money in an account earning 3.25% interest for 8 years. If the interest is compounded continuously, how much would she have in her account after 8 years? Jesse has saved $1800 from his last several birthdays. He would like to invest the money in an account that earns 5.375% interest for 7 years. If the interest is compounded continuously, how much money will Jesse have at the end of the 7 years? Jessica has earned $24800 from the sales of her books. She wants to invest the money in an account that earns 3.5% interest for 10 years. If the interest compounds continuously, how much will Jessica have in her account after 10 years?

Exponential Word Problem Practice Part 2 7. Kaitlyn has $2900 in credit card debt. Her credit card charges 11.75% interest, compounded continuously. How much will she owe on the balance if she does not make a payment for: a. 9 months? b. 2 years? c. 4 years? 8. Justin has $4200 in credit card debt. His card has an interest rate of 12.25% compounded continuously. How much would he owe if he didn’t pay on the balance for: a. 6 months? b. 1year? c. 3 years? Jane needs to make $6300 to help pay for a car. She is investing some money in an account that earns 4.125% interest that is compounded continuously. How much money must she invest if she is willing to wait: a. 3 years? b. 5 years? Kristen needs $2900 to pay for a computer. She is investing some money she has saved in an account that earns 3.875% compounded continuously. How much does she need to invest if she can wait: a. 2 years? b. 6 years? Jeremy needs $4200 to help put down money on a house. He is investing some money in an account that earns 5.25% interest, compounded continuously. How much does he need to invest to reach his goal if he can wait: a. 4 years? b. 8 years? 12. Andrea needs $10000 to help pay off some debts. She is investing some money in an account that earns 3.125% interest, compounded continuously. How much would she need to invest to reach this goal if she can wait: a. 5 years? b. 10 years?

Ticket out the door 4-25 Exponential word problems part 2 1. Mark has $2400 to invest. He can get an account for 5 years that earns 3.875% interest, compounded continuously. How much would he earn at the end of the 5 years? Michelle has $7200 she wants to invest. She can get an account earning 3.125% interest for 4 years. If the interest is compounded continuously, how much would Maggie have in her account at the end of the 4 years? Jeremy needs $7500 to put down on a car. If he can get an account earning 3.75% interest compounded continuously, how much would he need to invest if he could wait 3 years? Peg needs to make $5400 to put towards a down payment on a house. If she can get an account earning 5.25% interest compounded continuously, how much would she need to invest if she can wait 5 years?