### About Continuous Compound Interest Word Problems:

We sometimes need to solve a word problem that involves the continuous compound interest formula: A = Pe^{(rt)}. This formula is used when the number of compounding periods reaches a theoretical maximum.

Test Objectives

- Demonstrate an understanding of how to solve a word problem
- Demonstrate the ability to solve a continuous compound interest word problem

#1:

Instructions: Solve each word problem. Round your answer to the nearest hundredth.

a) Steve invests $2,807 in a 401(k) account with a fixed annual interest rate that is compounded continuously. After 13 years, the account balance reaches $9,044.13. What is the interest rate of the account?

Note: This problem requires the use of logarithms. An example is given here.

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#2:

Instructions: Solve each word problem. Round your answer to the nearest hundredth.

a) Adam invests $1,051 in a savings account with a fixed annual interest rate that is compounded continuously. After 8 years, the account balance reaches $1,698.49. What is the interest rate of the account?

Note: This problem requires the use of logarithms. An example is given here.

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#3:

Instructions: Solve each word problem. Round your answer to the nearest hundredth.

a) Daniel invests a lump sum of money in a savings account with a fixed annual interest rate of 5% that is compounded continuously. After 7 years, the account balance reaches $5,676.27. How much was initially invested?

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#4:

Instructions: Solve each word problem. Round your answer to the nearest hundredth.

a) Harry invests a lump sum of money in a bond fund with a fixed annual interest rate of 7% that is compounded continuously. After 17 years, the balance reaches $10,775.05. How much was initially invested?

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#5:

Instructions: Solve each word problem. Round your answer to the nearest hundredth.

a) Jacob invests a lump sum of money in a certificate of deposit account with a fixed annual interest rate of 7% that is compounded continuously. After 20 years, the account balance reaches $7,863.03. How much was initially invested?

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Written Solutions:

#1:

Solutions:

a) 9%

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#2:

Solutions:

a) 6%

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#3:

Solutions:

a) $4,000

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#4:

Solutions:

a) $3,278

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#5:

Solutions:

a) $1,939