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
