QuestionJune 8, 2025

Recently, a certain bank offered a 10-year CD that earns 2.9% compounded continuously. Use the given information to answer the questions. (a) If 20,000 is invested in this CD, how much will it be worth in 10 years? approximately square (Round to the nearest cent.)

Recently, a certain bank offered a 10-year CD that earns 2.9% compounded continuously. Use the given information to answer the questions. (a) If 20,000 is invested in this CD, how much will it be worth in 10 years? approximately square (Round to the nearest cent.)
Recently, a certain bank offered a 10-year CD that earns 2.9%  compounded continuously.
Use the given information to answer the questions.
(a) If 20,000 is invested in this CD, how much will it be worth in 10 years?
approximately square  (Round to the nearest cent.)

Solution
4.3(269 votes)

Answer

\26,735.40 Explanation 1. Identify the formula for continuous compounding Use the formula for continuous compounding: **A = Pe^{rt}**, where A is the amount, P is the principal, r is the rate, and t is the time. 2. Substitute the given values into the formula Here, P = 20000, r = 0.029, and t = 10. Substitute these values into the formula: A = 20000 \cdot e^{0.029 \cdot 10}. 3. Calculate the exponent Compute 0.029 \times 10 = 0.29. 4. Evaluate the exponential function Calculate e^{0.29} using a calculator to get approximately 1.33677. 5. Calculate the final amount Multiply the principal by the result from Step 4: A = 20000 \times 1.33677 \approx 26735.40.

Explanation

1. Identify the formula for continuous compounding<br /> Use the formula for continuous compounding: **$A = Pe^{rt}$**, where $A$ is the amount, $P$ is the principal, $r$ is the rate, and $t$ is the time.<br /><br />2. Substitute the given values into the formula<br /> Here, $P = 20000$, $r = 0.029$, and $t = 10$. Substitute these values into the formula: $A = 20000 \cdot e^{0.029 \cdot 10}$.<br /><br />3. Calculate the exponent<br /> Compute $0.029 \times 10 = 0.29$.<br /><br />4. Evaluate the exponential function<br /> Calculate $e^{0.29}$ using a calculator to get approximately $1.33677$.<br /><br />5. Calculate the final amount<br /> Multiply the principal by the result from Step 4: $A = 20000 \times 1.33677 \approx 26735.40$.
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