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

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

Understanding continuous compound interest helps students see how their money can grow, which is beneficial for financial planning.
Working on these problems improves students' use of exponential functions and logarithms, boosting overall math skills.
Solving those issues makes students assume cautiously and enhance their hassle-solving competencies, which might be critical for college and future jobs.
Learning approximately non-stop compound hobby enables college students make better selections about loans, financial savings, and investments.
These problems integrate math with economics and finance, helping college students see how distinct topics are associated and giving them a nicely-rounded education.

Determine the principal amount `(P)`, annual interest rate `(r)`, and time period in years `(t)` from the problem.
Apply the formula $ A = Pe^{rt} $, where $ A $ is the amount after time $ t $, $ P $ is the principal amount, $ r $ is the annual interest rate, and $ e $ is the base of the natural logarithm.
Compute $ e^{rt} $ to find the exponential growth factor.
Multiply the result from point `3` by the principal amount $ P $ to find the final amount $ A $.

Solved Example

Q. Bobby and Shelley deposit

\$800.00

into a savings account which earns

6\%

interest compounded continuously. They want to use the money in the account to go on a trip in

3

years. How much will they be able to spend?

\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 cent.

Solution:

Identify values for P, r, and t: Identify the values for P, r, and t. $\newline$ Principal amount $P$ = $\$800$ $\newline$ Rate of interest $r$ = $6\%$ or $0.06$ when expressed as a decimal $\newline$ Time in years $t$ = $3$ years
Calculate final amount using continuous compounding interest formula: Use the continuous compounding interest formula $A = Pe^{rt}$ to calculate the final amount. $\newline$ Substitute $P = 800$ , $r = 0.06$ , and $t = 3$ into the formula. $\newline$ $A = 800 \times e^{(0.06 \times 3)}$
Calculate exponent part of the formula: Calculate the exponent part of the formula. $0.06 \times 3 = 0.18$
Calculate $e$ raised to the power of $0.18$ : Calculate $e$ raised to the power of $0.18$ . $e^{0.18} \approx 2.71828^{0.18} \approx 1.1972173...$
Multiply principal amount by $e^{0.18}$ to find final amount: Multiply the principal amount by the value of $e$ raised to the power of $0.18$ to find the final amount. $\newline$ $A = 800 \times 1.1972173...$ $\newline$ $A \approx 800 \times 1.1972173 \approx 957.77384$
Round final amount to nearest cent: Round the final amount to the nearest cent. $A \approx \$957.77$