QuestionMay 24, 2025

Use the appropriate interest formula to find the amount that will be in an account, given the stated conditions. An initial investment of 12,000 is invested at an interest rate of 7% compounded continuously for 5 years.

Use the appropriate interest formula to find the amount that will be in an account, given the stated conditions. An initial investment of 12,000 is invested at an interest rate of 7% compounded continuously for 5 years.
Use the appropriate interest formula to find the amount that will be in an account, given the
stated conditions. An initial investment of 12,000 is invested at an interest rate of 7% 
compounded continuously for 5 years.

Solution
4.4(167 votes)

Answer

\17,028.80 Explanation 1. Identify the formula for continuous compounding Use the formula for continuous compounding: **A = Pe^{rt}**, where P is the principal, r is the rate, and t is time. 2. Substitute the given values Substitute P = 12000, r = 0.07, and t = 5 into the formula: A = 12000 \cdot e^{0.07 \cdot 5}. 3. Calculate the exponent Compute 0.07 \times 5 = 0.35. 4. Compute the exponential function Calculate e^{0.35} using a calculator to get approximately 1.419067. 5. Calculate the final amount Multiply the result by the principal: A = 12000 \times 1.419067 \approx 17028.80.

Explanation

1. Identify the formula for continuous compounding<br /> Use the formula for continuous compounding: **$A = Pe^{rt}$**, where $P$ is the principal, $r$ is the rate, and $t$ is time.<br /><br />2. Substitute the given values<br /> Substitute $P = 12000$, $r = 0.07$, and $t = 5$ into the formula: $A = 12000 \cdot e^{0.07 \cdot 5}$.<br /><br />3. Calculate the exponent<br /> Compute $0.07 \times 5 = 0.35$.<br /><br />4. Compute the exponential function<br /> Calculate $e^{0.35}$ using a calculator to get approximately $1.419067$.<br /><br />5. Calculate the final amount<br /> Multiply the result by the principal: $A = 12000 \times 1.419067 \approx 17028.80$.
Click to rate:

Similar Questions