QuestionJune 29, 2025

What is the present value (principal) of the investment amount that grows to 24,300 in 5 years if the interest rate is 7% compounded continuously? 17,123.92 18,290.80 18,275.83 17,768.65

What is the present value (principal) of the investment amount that grows to 24,300 in 5 years if the interest rate is 7% compounded continuously? 17,123.92 18,290.80 18,275.83 17,768.65
What is the present value (principal) of the investment amount that grows to 24,300
in 5 years if the interest rate is 7%  compounded continuously?
 17,123.92
 18,290.80
 18,275.83
 17,768.65

Solution
4.6(289 votes)

Answer

\18,275.83 Explanation 1. Identify the formula for continuous compounding Use the formula for continuous compounding: A = Pe^{rt}, where A is the future value, P is the principal, r is the interest rate, and t is the time in years. 2. Rearrange the formula to solve for principal Rearrange to find P: P = \frac{A}{e^{rt}}. 3. Substitute values into the formula Substitute A = 24300, r = 0.07, and t = 5: P = \frac{24300}{e^{0.07 \times 5}}. 4. Calculate the exponent Calculate e^{0.35} using a calculator. 5. Compute the principal Divide 24300 by the result from Step 4.

Explanation

1. Identify the formula for continuous compounding<br /> Use the formula for continuous compounding: $A = Pe^{rt}$, where $A$ is the future value, $P$ is the principal, $r$ is the interest rate, and $t$ is the time in years.<br />2. Rearrange the formula to solve for principal<br /> Rearrange to find $P$: $P = \frac{A}{e^{rt}}$.<br />3. Substitute values into the formula<br /> Substitute $A = 24300$, $r = 0.07$, and $t = 5$: $P = \frac{24300}{e^{0.07 \times 5}}$.<br />4. Calculate the exponent<br /> Calculate $e^{0.35}$ using a calculator.<br />5. Compute the principal<br /> Divide $24300$ by the result from Step 4.
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