QuestionMay 22, 2025

Question 4 (1 point) Kimi invests 4,000 into an account that earns 3% annual interest com __ (round to two decimal places) compounded continuously. y. The amount of money in Kimi's account after 5 years is Blank 1: square

Question 4 (1 point) Kimi invests 4,000 into an account that earns 3% annual interest com __ (round to two decimal places) compounded continuously. y. The amount of money in Kimi's account after 5 years is Blank 1: square
Question 4 (1 point)
Kimi invests 4,000 into an account that earns 3%  annual interest com
__ (round to two decimal places)
compounded continuously. y. The amount of money in Kimi's account after 5 years is
Blank 1: square

Solution
4.5(195 votes)

Answer

4647.34 Explanation 1. Identify the formula for continuous compounding Use the formula for continuous compounding: **A = Pe^{rt}**, where P is the principal amount, r is the interest rate, and t is the time in years. 2. Substitute values into the formula Here, P = 4000, r = 0.03, and t = 5. Substitute these values into the formula: A = 4000 \cdot e^{0.03 \cdot 5}. 3. Calculate the exponent Compute the exponent: 0.03 \times 5 = 0.15. 4. Evaluate the exponential function Calculate e^{0.15} using a calculator to get approximately 1.16183424. 5. Calculate the final amount Multiply by the principal: A = 4000 \times 1.16183424 = 4647.34.

Explanation

1. Identify the formula for continuous compounding<br /> Use the formula for continuous compounding: **$A = Pe^{rt}$**, where $P$ is the principal amount, $r$ is the interest rate, and $t$ is the time in years.<br /><br />2. Substitute values into the formula<br /> Here, $P = 4000$, $r = 0.03$, and $t = 5$. Substitute these values into the formula: $A = 4000 \cdot e^{0.03 \cdot 5}$.<br /><br />3. Calculate the exponent<br /> Compute the exponent: $0.03 \times 5 = 0.15$.<br /><br />4. Evaluate the exponential function<br /> Calculate $e^{0.15}$ using a calculator to get approximately $1.16183424$.<br /><br />5. Calculate the final amount<br /> Multiply by the principal: $A = 4000 \times 1.16183424 = 4647.34$.
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