Question $3$

Molly inherited $\backslash (\backslash$$ $5000\backslash )$ and decided to start a lawn$-$mowing service. With her inheritance and a bank loan of $\backslash (\backslash$$ $5000\backslash ),$ she bought a used ride$-$on lawnmower and a used truck. For five years, Molly had a gross income of $\backslash (\backslash$$ $30000\backslash ),$ which covered the annual operating costs and the loan payment, both of which totaled $\backslash (\backslash$$ $4500\backslash ).$ She spent the rest of her income personally. At the end of five years, Molly found that her loan was paid off but the equipment was wearing out.

a$)$ If the equipment $($lawnmower and truck$)$ was depreciating at the rate of $50$ percent according to the declining$-$balance method, what is its book value after five years?

$($b$)$ If Molly wanted to avoid being left with a worthless lawnmower and truck and with no money for renewing them at the end of five years, how much should she have saved annually toward the second set of used lawnmower and used truck of the same initial value as the first set? Assume that Molly's first lawnmower and truck could be sold at their book value. Use an interest rate of $7$ percent.