Question

suppose that $11,000 is invested in a bond fund and the account grows to $14,243.93 in 5 yr.
part: 0 / 2
part 1 of 2
(a) use the model $a = pe^{rt}$ to determine the average rate of return under continuous compounding. round to the nearest tenth of a percent. avoid rounding in intermediate steps.
the average rate of return under continuous compounding is approximately $square%$.

Explanation:

Step1: Substitute the values into the formula

Given \( A = 14243.93 \), \( P = 11000 \), \( t = 5 \), substitute into \( A=Pe^{rt} \). So, \( 14243.93 = 11000e^{5r} \).

Step2: Solve for \( e^{5r} \)

Divide both sides by \( 11000 \): \( \frac{14243.93}{11000}=e^{5r} \), which simplifies to \( 1.2949027 = e^{5r} \).

Step3: Take the natural logarithm of both sides

Using \( \ln(e^{x})=x \), we have \( \ln(1.2949027)=5r \).

Step4: Solve for \( r \)

Calculate \( \ln(1.2949027)\approx0.26 \). Then \( r=\frac{0.26}{5}=0.052 \).

Step5: Convert \( r \) to a percentage

Multiply \( r \) by \( 100 \): \( 0.052\times100 = 5.2\% \).

Answer:

\( 5.2 \)