Find Time In Continuous Compound Interest Word Problems Worksheets [PDF]: Algebra 2 Math

How Will This Worksheet on 'Find Time in Continuous Compound Interest Word Problems' Benefit Your Student's Learning?

Enhances students' ability to think critically and logically by manipulating and interpreting complex mathematical formulas.
Helps students make informed financial decisions, such as planning for savings and investments, by understanding how to calculate the time required for investments to grow.
Improves analytical skills by breaking down word problems into smaller, manageable parts and using the correct math formulas.
Builds confidence in math skills, encouraging students to tackle more challenging concepts and problems.

Determine the final amount `(A)`, the principal amount `(P)`, and the annual interest rate `(r)` from the problem.
Use the continuous compound interest formula $ A = Pe^{rt} $.
Divide both sides of the equation by $ P $ to get `\frac{A}{P} = e^{rt}`.
Take the natural logarithm of both sides and solve for $ t $ using `t = \frac{\ln(\frac{A}{P})}{r}`.

Solved Example

Q. Emily received a bonus of

\$9,000

from her company and wants to invest it in an account to save for a dream vacation. Her investment account has a

10\%

interest rate compounded continuously. How long will it take for her money to grow to

\$24,420

?

\newline

Use the formula

A = Pe^{rt}

, where

A

is the balance (final amount),

P

is the principal (starting amount),

e

is the base of natural logarithms (

\approx 2.71828

r

is the interest rate expressed as a decimal, and

t

is the time in years.

\newline

Round your answer to the nearest tenth.

Solution:

Identify values: Identify the values for $P$ , $A$ , $r$ , and $t$ . $\newline$ $P = 9000$ $\newline$ $A = 24420$ $\newline$ $r = 0.10$
Use formula: Use the formula $A = Pe^{rt}$ . $\newline$ $24420 = 9000 \times e^{0.10 \times t}$
Divide to isolate: Divide both sides by $9000$ to isolate $e^{0.10 \times t}$ . $\newline$ $\frac{24420}{9000} = e^{0.10 \times t}$ $\newline$ $2.7133333 = e^{0.10 \times t}$
Take natural logarithm: Take the natural logarithm of both sides to solve for $t$ . $\newline$ $\ln(2.7133333) = 0.10 \cdot t$
Calculate logarithm: Calculate the natural logarithm. $\ln(2.7133333) \approx 0.998$ $\newline$ $0.998 = 0.10 \cdot t$
Solve for $t$ : Solve for $t$ by dividing both sides by $0.10$ . $\newline$ $t = \frac{0.998}{0.10}$ $\newline$ $t \approx 9.98$
Round to nearest tenth: Round to the nearest tenth. $\newline$ $t \approx 10.0$ $\newline$ So, it will take approximately 10.0 years for Emily's money to grow.