The problem describes an investment made by Jolene, with a principal of $9250, an interest rate of 6.3% compounded annually. The accrued value $A$ after $t$ years is given by the formula $A = 9250(1.063)^t$. We need to determine the value of Jolene's investment after 11 years, and the number of years it will take for the investment to reach $40081.14.

1. Problem Description

The problem describes an investment made by Jolene, with a principal of $9250, an interest rate of 6.3$A$after$t$years is given by the formula$A = 9250(1.063)^t$. We need to determine the value of Jolene's investment after 11 years, and the number of years it will take for the investment to reach$40081.

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2. Solution Steps

First, we need to determine the amount Jolene will have after 11 years. We substitute $t = 11$ into the formula:

$A = 9250(1.063)^{11}$

$A = 9250 \times 2.0012179$

$A = 18511.256775$

Rounding to two decimal places, we get $A = 18511.26$.

Next, we need to find how long it will take for Jolene to have $40081.

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4. We substitute $A = 40081.14$ into the formula and solve for $t$:

$40081.14 = 9250(1.063)^t$

Divide both sides by 9250:

$\frac{40081.14}{9250} = (1.063)^t$

$4.3331 = (1.063)^t$

To solve for $t$, we take the natural logarithm of both sides:

$ln(4.3331) = ln((1.063)^t)$

$ln(4.3331) = t \times ln(1.063)$

$t = \frac{ln(4.3331)}{ln(1.063)}$

$t = \frac{1.4664}{0.0611}$

$t \approx 23.999$

Rounding to the nearest whole year, we get $t = 24$ years.

3. Final Answer

After 11 years, Jolene will have $18511.26 in her savings account.

Jolene will have accrued $40081.14 in her savings after 24 years.