Find Amount After Compound Interest Word Problems Worksheets [PDF]: Algebra 2 Math

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.

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:

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).
Substitute Values: Substitute the values into the compound interest formula. $A = 100(1 + (0.09)/(1))^{(1\times5)}$
Simplify Expression: Simplify the expression inside the parentheses and then calculate the exponent. $\newline$ $A = 100(1 + 0.09)^5$ $\newline$ $A = 100(1.09)^5$
Calculate Exponent: Calculate the value of $(1.09)^5$ . $(1.09)^5 \approx 1.53862$ (rounded to five decimal places for intermediate calculation)
Find Final Balance: Multiply the principal by the result from Step $4$ to find the final balance. $\newline$ $A = 100 \times 1.53862$ $\newline$ $A \approx 153.862$
Round Final Balance: Round the final balance to the nearest cent. $A \approx \$(153.86)$