# Find Amount After Continuous Compound Interest Word Problems Worksheet

## 6 problems

To find amount after continuous compound interest, we use the formula $$A = Pe^{rt}$$, where $$A$$ is amount after time $$t$$, $$P$$ is the principal amount, $$r$$ is annual interest rate, and $$e$$ is the base of the natural logarithm.

Example: Deborah and Abu 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?

Algebra 2
Exponential Functions

## 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.

## How to Find Amount After Continuous Compound Interest Word Problems?

• 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:
1. 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
2. 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$$A = 800 \times e^{(0.06 \times 3)}$
3. Calculate exponent part of the formula: Calculate the exponent part of the formula. $0.06 \times 3 = 0.18$
4. Calculate $e$ raised to the power of $0.18$: Calculate $e$ raised to the power of $0.18$.$e^{0.18} \approx 2.71828^{0.18} \approx 1.1972173...$
5. Multiply principal amount by $e^{0.18}$ to find final amount: Multiply the principal amount by the value of $e$ raised to the power of $0.18$ to find the final amount.$\newline$$A = 800 \times 1.1972173...$$\newline$$A \approx 800 \times 1.1972173 \approx 957.77384$
6. Round final amount to nearest cent: Round the final amount to the nearest cent. $A \approx \957.77$

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