Questions: If 2000 is invested at 5% compounded continuously, what is the amount after 7 years? Which of the following is the appropriate formula with the correct values substituted? Select the correct choice below and, if necessary, fill in A. A=P(1+rt), with P=, r=, and t= B. A=P(1+i)^n, with P=, i=, and n= C. A=Pe^rt, with P=, r=, and t=

If 2000 is invested at 5% compounded continuously, what is the amount after 7 years?

Which of the following is the appropriate formula with the correct values substituted? Select the correct choice below and, if necessary, fill in
A. A=P(1+rt), with P=, r=, and t=

B. A=P(1+i)^n, with P=, i=, and n=

C. A=Pe^rt, with P=, r=, and t=
Transcript text: If $\$ 2000$ is invested at $5 \%$ compounded continuously, what is the amount after 7 years? Which of the following is the appropriate formula with the correct values substituted? Select the correct choice below and, if necessary, fill in A. $A=P(1+r t)$, with $P=\square, r=\square$, and $t=$ $\square$ $\square$ $\square$ B. $A=P(1+i)^{n}$, with $P=\square, i=\square$, and $n=$ $\square$ C. $\mathrm{A}=\mathrm{P} e^{\mathrm{rt}}$, witi $\mathrm{P}=$ $\square$ , $r=$ $\square$ , and $\mathrm{t}=$ $\square$
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Solution

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Solution Steps

Step 1: Identify the Formula for Continuous Compounding

The formula for continuous compounding is given by: \[ A = Pe^{rt} \]

Step 2: Substitute the Given Values into the Formula

Given:

  • Principal, \( P = 2000 \)
  • Rate, \( r = 0.05 \) (5% as a decimal)
  • Time, \( t = 7 \) years

Substitute these values into the formula: \[ A = 2000 \cdot e^{0.05 \cdot 7} \]

Step 3: Select the Correct Choice

From the given choices, the correct formula with values substituted is: C. \( A = Pe^{rt} \), with \( P = 2000 \), \( r = 0.05 \), and \( t = 7 \)

Final Answer

C. \( A = Pe^{rt} \), with \( P = 2000 \), \( r = 0.05 \), and \( t = 7 \)

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