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Question 20, 8.4.31
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Suppose Christian stops for coffee a given number of times a week. Use the information in the following table to calculate how much Christian would save if he deposited the amount he would spend on coffee into an ordinary annuity instead. Assume there are four weeks in a month.
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Christian would have $\mathrm{\$}◻$ in the annuity. (Round to the nearest cent as needed.)

Step 1 ：Given that Christian buys 9 cups of coffee per week, with each cup costing $4.05, the total amount he spends on coffee each week is $9\times 4.05=36.45$ dollars.

Step 2 ：The annual interest rate for the annuity is 2.8%, which is equivalent to 0.028. Since there are 52 weeks in a year, the weekly interest rate is $0.028/52=0.0005384615384615384$.

Step 3 ：Christian plans to deposit the amount he would spend on coffee into the annuity for 14 years. Since there are 52 weeks in a year, the total number of periods is $14\times 52=728$ weeks.

Step 4 ：We can now calculate the future value of the annuity using the formula: $FV=P\times [(1+r{)}^{nt}-1]/r$, where FV is the future value of the annuity, P is the payment per period, r is the interest rate per period, n is the number of periods, and t is the time in years.

Step 5 ：Substituting the given values into the formula, we get: $FV=36.45\times [(1+0.0005384615384615384{)}^{728}-1]/0.0005384615384615384$.

Step 6 ：Solving the equation gives us the future value of the annuity, which is approximately $32,477.79.

Step 7 ：Thus, if Christian deposited the amount he would spend on coffee into an ordinary annuity instead, he would have $\boxed{{\displaystyle 32,477.79}}$ dollars in the annuity after 14 years.