Answer:
[tex]\large \boxed{\$229}}[/tex]
Step-by-step explanation:
1. Calculate the time for Joshua's investment to double
The formula for interest compounded annually is
A = P(1 + r)ᵗ
where
A = Accrued Amount
P = Principal Amount
r =annual interest rate as a decimal
t = time in years
(a) Data
A = $220
P = $110
r =0.025
(b) Calculation
[tex]\begin{array}{rcl}A & = & P(1 + r)^{t}\\220 & = & 110(1+ 0.025)^{t}\\2 & = & 1.025^{t}\\\ln 2 & = & t \ln 1.025\\t & = & \dfrac{\ln 2}{\ln 1.025}\\\\t & = & \dfrac{0.6931}{0.02469}\\\\t & = & \textbf{28.07 yr}\\\\\end{array}[/tex]
It will take 28.07 yr for Joshua to double his investment.
2. Calculate the value of Zoey's investment
The formula for interest compounded continuously is
[tex]\begin{array}{rcl}A & = & Pe^{rt}\\& = & 110e^{0.02625\times 28.07}\\& = & 110e^{0.7368}\\& = & 110\times2.0893\\& = & \mathbf{\$229}\\\end{array}\\\text{Zoey will have $\large \boxed{\mathbf{\$229}}$ in her account by the time Joshua's money has doubled.}[/tex]
