$13$ Write an algorithm to settle the following question: A bank account starts out with $$10,000.$ Interest is compounded monthly at $6$ percent per year $(0\mathrm{.}5$ percent per month$).$ Every month, $$500$ is withdrawn to meet college expenses. After how many years is the account depleted?

$14$ Consider the question in Exercise R$1\mathrm{.}13.$ Suppose the numbers $($ $$10,000,6$ percent, $$500)$ were user selectable. Are there values for which the algorithm you developed would not terminate? If so$,$ change the algorithm to make sure it always terminates.

$15$ In order to estimare the cost of painting a house, a painter needs to know the surface area of the exterior. Develop an algorithm for computing that value. Your inputs are the width, length, and height of the bouse, the number of windows and doors, and their dimensions. $($Assume the windows and doors have a uniform size.$)$

$16$ In How To $1\mathrm{.}1,$ you made assumptions about the price of gas and annual usage to compare cars. Ideally, you would like to know which car is the better deal without making these assumptions. Why can't a computer program solve that problem?

$17$ Suppose you put your younger brother in charge of backing up your work. Write a set of derailed instructions for carrying out his task. Explain how often he should do it$,$ and what files he needs to copy from which folder to which location. Explain how he should verify that the backup was carried out correctly,

$18$ Write pseudocode for an algorithm thar describes how to prepare Sunday breakfast in your household.

$19$ The ancient Babylonians had an algorithm for determining the square root of a number $4.$ Start with an initial guess of $\frac{a}{2}.$ Then find the average of your guess $g$ and a$/$g$.$ That's your next guess. Repeat until two consecutive guesses are close enough. Write pscudocode for this algorithm.