Find Amount After Continuous Compound Interest Word Problems Worksheet

Algebra 2
Exponential Functions

Total questions - 6

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How Will This Worksheet on "Find Amount After Continuous Compound Interest Word Problems" Benefit Your Student's Learning?

  • Understanding continuous compound interest helps students see how their money can grow, which is beneficial for financial planning.
  • Working on these problems improves students' use of exponential functions and logarithms, boosting overall math skills.
  • Solving those issues makes students assume cautiously and enhance their hassle-solving competencies, which might be critical for college and future jobs.
  • Learning approximately non-stop compound hobby enables college students make better selections about loans, financial savings, and investments.
  • These problems integrate math with economics and finance, helping college students see how distinct topics are associated and giving them a nicely-rounded education.

How to Find Amount After Continuous Compound Interest Word Problems?

  • Determine the principal amount `(P)`, annual interest rate `(r)`, and time period in years `(t)` from the problem.
  • Apply the formula \( A = Pe^{rt} \), where \( A \) is the amount after time \( t \), \( P \) is the principal amount, \( r \) is the annual interest rate, and \( e \) is the base of the natural logarithm.
  • Compute \( e^{rt} \) to find the exponential growth factor.
  • Multiply the result from point `3` by the principal amount \( P \) to find the final amount \( A \).

Solved Example

Q. Bobby and Shelley deposit $800.00\$800.00 into a savings account which earns 6%6\% interest compounded continuously. They want to use the money in the account to go on a trip in 33 years. How much will they be able to spend?\newlineUse the formula A=PertA = Pe^{rt}, where AA is the balance (final amount), PP is the principal (starting amount), ee is the base of natural logarithms (2.71828\approx 2.71828), rr is the interest rate expressed as a decimal, and tt is the time in years.\newlineRound your answer to the nearest cent.
Solution:
  1. Identify values for P, r, and t: Identify the values for P, r, and t.\newlinePrincipal amount PP = $800\$800 \newlineRate of interest rr = 6%6\% or 0.060.06 when expressed as a decimal \newlineTime in years tt = 33 years
  2. Calculate final amount using continuous compounding interest formula: Use the continuous compounding interest formula A=PertA = Pe^{rt} to calculate the final amount.\newlineSubstitute P=800P = 800, r=0.06r = 0.06, and t=3t = 3 into the formula.\newlineA=800×e(0.06×3)A = 800 \times e^{(0.06 \times 3)}
  3. Calculate exponent part of the formula: Calculate the exponent part of the formula. 0.06×3=0.180.06 \times 3 = 0.18
  4. Calculate ee raised to the power of 0.180.18: Calculate ee raised to the power of 0.180.18.e0.182.718280.181.1972173...e^{0.18} \approx 2.71828^{0.18} \approx 1.1972173...
  5. Multiply principal amount by e0.18e^{0.18} to find final amount: Multiply the principal amount by the value of ee raised to the power of 0.180.18 to find the final amount.\newlineA=800×1.1972173...A = 800 \times 1.1972173...\newlineA800×1.1972173957.77384A \approx 800 \times 1.1972173 \approx 957.77384
  6. Round final amount to nearest cent: Round the final amount to the nearest cent. A$957.77A \approx \$957.77
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About Worksheet

Algebra 2
Exponential Functions

To find amount after continuous compound interest, we use the formula \( A = Pe^{rt} \), where \( A \) is amount after time \( t \), \( P \) is the principal amount, \( r \) is annual interest rate, and \( e \) is the base of the natural logarithm.

Example: Deborah and Abu deposit \(\$800.00\) into a savings account which earns \(6\%\) interest compounded continuously. They want to use the money in the account to go on a trip in \(3\) years. How much will they be able to spend?

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