The problem provides an equation to calculate the accrued value $A$ of an investment made by Jolene: $A = 18600(1.071)^t$, where $t$ is the length of the investment in years. We are asked to: a) Determine the amount of money Jolene will have after 16 years, rounded to two decimal places. b) Determine how long it will take for Jolene to have $118,530.10 accrued, rounded to the nearest whole year.

1. Problem Description

The problem provides an equation to calculate the accrued value $A$ of an investment made by Jolene: $A = 18600(1.071)^t$, where $t$ is the length of the investment in years.

We are asked to:

a) Determine the amount of money Jolene will have after 16 years, rounded to two decimal places.

b) Determine how long it will take for Jolene to have $118,530.10 accrued, rounded to the nearest whole year.

2. Solution Steps

a) To find the amount of money Jolene will have after 16 years, we substitute $t = 16$ into the equation:

$A = 18600(1.071)^{16}$

$A = 18600(3.02276)$

$A = 56223.336$

Rounding to two decimal places, we get $A = 56223.34$.

b) To find how long it will take for Jolene to have $118,530.10 accrued, we set$A = 118530.10$and solve for$t$:

$118530.10 = 18600(1.071)^t$

Divide both sides by 18600:

$\frac{118530.10}{18600} = (1.071)^t$

$6.372586 = (1.071)^t$

Take the natural logarithm of both sides:

$ln(6.372586) = ln((1.071)^t)$

$ln(6.372586) = t * ln(1.071)$

$t = \frac{ln(6.372586)}{ln(1.071)}$

$t = \frac{1.8524}{0.0685}$

$t = 27.03$

Rounding to the nearest whole year, we get $t = 27$.

3. Final Answer

Answer: After 16 years, Jolene will have $56223.34 in her savings account. (Round to TWO decimal places.)

Answer: Jolene will have accrued $118,530.10 in her savings after 27 years. (Round to the nearest whole year.)