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EXAMPLE 5

Finance. You deposit $4000 in an account that pays 6% annual interest compounded continuously. What is the balance after 1 year?. A. Pe rt. =. =. 4000. e 0.06(1). 4247.35. ANSWER. The balance at the end of 1 year is $4247.35. EXAMPLE 5. Model continuously compounded interest.

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EXAMPLE 5

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  1. Finance You deposit $4000 in an account that pays 6% annual interest compounded continuously. What is the balance after 1year? A Pert = = 4000 e0.06(1) 4247.35 ANSWER The balance at the end of 1 year is $4247.35. EXAMPLE 5 Model continuously compounded interest SOLUTION Use the formula for continuously compounded interest. Write formula. Substitute 4000 for P, 0.06 for r, and 1 for t. Use a calculator.

  2. A Pert = = 2500 e0.05 2 = 2500 e0.10 = 2500 1.105 2762.9 ANSWER The balance at the end of 2 years is $2762.9. for Example 5 GUIDED PRACTICE FINANCE:You deposit $2500 in an account that pays 5% annual interest compounded continuously. Find the balance after each amount of time? a. 2years SOLUTION Use the formula for continuously compounded interest. Write formula. Substitute 2500 for P, 0.05 for r, and 2 for t.

  3. A Pert = = 2500 e0.05 5 = 2500 e0.25 = 2500 1.2840 3210.06 ANSWER The balance at the end of 5 years is $3210.06. for Example 5 GUIDED PRACTICE FINANCE:You deposit $2500 in an account that pays 5% annual interest compounded continuously. Find the balance after each amount of time? b. 5years SOLUTION Use the formula for continuously compounded interest. Write formula. Substitute 2500 for P, 0.05 for r and 5 for t.

  4. A Pert = = 2500 e0.05 7.5 = 2500 e0.375 = 2500 1.459 3637.48 ANSWER The balance at the end of 7.5 year is $3637.48. for Example 5 GUIDED PRACTICE FINANCE:You deposit $2500 in an account that pays 5% annual interest compounded continuously. Find the balance after each amount of time? c. 7.5years SOLUTION Use the formula for continuously compounded interest. Write formula. Substitute 2500 for P, 0.05 for r and 7.5 for t.

  5. a. A 2500 = The amount of interest balance – deposit = – $2762.93 $2500 = $262.93 = for Example 5 GUIDED PRACTICE 11. FINANCE: Find the amount of interest earned in parts (a) – (c) of Exercise 10. SOLUTION The balance at the end of 2 years is $2762.93.

  6. b. A 2500 = The amount of interest balance – deposit = – $3210.06 $2500 = $710.06 = for Example 5 GUIDED PRACTICE 11. FINANCE: Find the amount of interest earned in parts (a) – (c) of Exercise 10. SOLUTION The balance at the end of 5 years is $3210.06.

  7. c. A 2500 = The amount of interest balance – deposit = – $3637.48 $2500 = $1137.48 = for Example 5 GUIDED PRACTICE 11. FINANCE: Find the amount of interest earned in parts (a) – (c) of Exercise 10. SOLUTION The balance at the end of 7.5 years is $3637.48.

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