Find Rate Of Interest In Compound Interest Word Problems Worksheets [PDF]: Algebra 2 Math

How Will This Worksheet on "Find Rate of Interest in Compound Interest Word Problems" Benefit Your Student's Learning?

Solving these problems enhances critical thinking and analytical skills as students learn to interpret information and apply mathematical concepts effectively.
It reinforces the application of mathematical formulas, helping students practice their algebraic manipulation and problem-solving abilities.
These problems are common in everyday life, such as savings accounts and loans, making the math more relatable and engaging for students.
Learning to calculate interest rates enables students to make informed decisions about loans, savings, and investments, promoting responsible financial habits.

Note the principal amount $ P $, the final amount $ A $, the compounding frequency per year $ n $, and the time period $ t $ in years.
Apply the formula `r = n \left(\frac{A}{P}\right)^{\frac{1}{nt}} - 1` to calculate the annual interest rate $ r $.
Plug the known values into the formula step-by-step.
Understand the calculated interest rate $ r $ within the context of the problem, indicating the percentage rate at which the principal grows over time with compound interest.

Solved Example

Q. You invested

\$3,000

in a savings account, and after

5

years, the balance grew to

\$4,665

. The interest is compounded annually. What is the annual interest rate

?

\newline

Use the formula

A = P\left(1 + \frac{r}{n}\right)^{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 tenth.

Solution:

Identify values: Identify the values of $A$ , $P$ , $n$ , and $t$ .
A = $\$4,665$
P = $\$3,000$
n = $1$ (compounded annually)
t = $5$ years
Use formula: Use the formula $A = P\left(1 + \frac{r}{n}\right)^{nt}$ and substitute the values. $\newline$ $4665 = 3000\left(1 + \frac{r}{1}\right)^{1 \cdot 5}$ $\newline$ $4665 = 3000(1 + r)^5$
Isolate $(1 + r)^5$ : $\newline$ Divide both sides by $3,000$ to isolate $(1 + r)^5$ . $\newline$ $\frac{4,665}{3,000} = (1 + r)^5$ $\newline$ $1.555 = (1 + r)^5$
Take fifth root: Take the fifth root of both sides to solve for $(1 + r)$ . $\newline$ $(1.555)^{\frac{1}{5}} = 1 + r$ $1.092 = 1 + r$
Solve for $r$ : Subtract $1$ from both sides to solve for $r$ . $\newline$ $1.092 - 1 = r$ $\newline$ $r = 0.092$
Convert to percentage: Convert $r$ to a percentage by multiplying by $100$ . $\newline$ $0.092\times 100 = 9.2\%$ The annual interest rate, rounded to the nearest tenth, is approximately $9.2\%$ .