Compound Interest Part 2 CONTINUOUSLY COMPOUNDED INTEREST New

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, 2 nd 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: a. 4 years? b. 7 years? c. 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? 3. 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? 4. 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? 5. 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? 6. 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. 1 year? c. 3 years? 9. 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? 10. 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? 11. 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 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? 2. 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? 3. 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? 4. 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?