# Find Amount After Compound Interest Word Problems Worksheet

## 6 problems

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.

Algebra 2
Exponential Functions

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

### What teachers are saying about BytelearnWhat teachers are saying

Stephen Abate
19-year math teacher
Carmel, CA
Any math teacher that I know would love to have access to ByteLearn.
Jennifer Maschino
4-year math teacher
Summerville, SC
“I love that ByteLearn helps reduce a teacher’s workload and engages students through an interactive digital interface.”
Rodolpho Loureiro
Dean, math program manager, principal
Miami, FL
“ByteLearn provides instant, customized feedback for students—a game-changer to the educational landscape.”