Find Amount After Compound Interest Word Problems Worksheet

Algebra 2
Exponential Functions

Total questions - 6

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

  • Helps grasp how compound interest impacts money saved or invested, important for managing personal finances.
  • Uses math to solve real-life problems like loans, investments, and savings, making financial concepts easier to understand.
  • Develops skills to handle complex financial scenarios with varying interest rates and compounding frequencies.
  • Encourages looking at different ways interest is added to decide how best to plan for the future.
  • Makes math skills stronger by using formulas to solve real problems and figure out how much money can be made.
  • Shows how to guess how much money will be saved or invested in the future using compound interest.

How to Find Amount After Compound Interest Word Problems?

  • Note the principal amount \( P \), annual interest rate \( r \), number of times interest compounds per year \( n \), and time period \( t \) in years.
  • Utilize `A = P \left(1 + \frac{r}{n}\right)^{nt}` to calculate the final amount \( A \) after compound interest.
  • Substitute the values into the formula and perform the calculations sequentially to find the total amount including interest.
  • Understand the meaning of the final amount \( A \) within the context of the problem, considering how compound interest affects the principal over time.

Solved Example

Q. Steven opened a savings account and deposited $100.00\$100.00 as principal. The account earns 9%9\% interest, compounded annually. What is the balance after 55 years?\newlineUse the formula A=P(1+rn)ntA = P(1 + \frac{r}{n})^{nt}, where AA is the balance (final amount), PP is the principal (starting amount), rr is the interest rate expressed as a decimal, nn is the number of times per year that the interest is compounded, and tt is the time in years.\newlineRound your answer to the nearest cent.
Solution:
  1. Identify Variables: Identify the values for the variables in the compound interest formula A=P(1+rn)ntA = P(1 + \frac{r}{n})^{nt}. Here, P=$100P = \$100 (the principal), r=9%r = 9\% or 0.090.09 (the interest rate as a decimal), n=1n = 1 (since the interest is compounded annually), and t=5t = 5 years (the time period).
  2. Substitute Values: Substitute the values into the compound interest formula. A=100(1+(0.09)/(1))(1×5)A = 100(1 + (0.09)/(1))^{(1\times5)}
  3. Simplify Expression: Simplify the expression inside the parentheses and then calculate the exponent. \newlineA=100(1+0.09)5A = 100(1 + 0.09)^5\newlineA=100(1.09)5A = 100(1.09)^5
  4. Calculate Exponent: Calculate the value of (1.09)5(1.09)^5.(1.09)51.53862(1.09)^5 \approx 1.53862 (rounded to five decimal places for intermediate calculation)
  5. Find Final Balance: Multiply the principal by the result from Step 44 to find the final balance.\newlineA=100×1.53862A = 100 \times 1.53862\newlineA153.862A \approx 153.862
  6. Round Final Balance: Round the final balance to the nearest cent. A$(153.86)A \approx \$(153.86)
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About Worksheet

Algebra 2
Exponential Functions

Find amount after compound interest word problems involve calculating total funds accrued with compound interest, using `A = P \left(1 + \frac{r}{n}\right)^{nt}`. Here, \( A \) is the final amount, \( P \) is the principal, \( r \) is the annual interest rate, \( n \) is the number of times interest compounds per year, and \( t \) is time in years. Explore examples in find amount after compound interest word problems pdf for detailed practice and solutions.

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