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=
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 $\mathrm{t}=$ $\square$
Solution
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 \( t = 7 \)