A method for calculating the interest owed on a credit card is the daily balance method.

The daily balance is calculated at the end of each day. To get a daily balance, we take the balance at the end of the previous day and add the simple interest on the previous day's balance $($need to determine the appropriate value for time$).$ We then add or subtract any purchases, credits, or payments that were made that day. The balance subject to Interest Rate at the end of the billing cycle is the average of the daily balances. Use $365$ days to represent a year.

Use the daily balance method to answer the following questions:

A credit card has an annual interest rate of $18\mathrm{.}99\backslash \%.$ In a $30-$day billing cycle, purchases of $\backslash$$$345\mathrm{.}96$ and $\backslash (\backslash$$ $296\mathrm{.}71\backslash )$ were made on days $9$ and $16$ respectively, and a payment of $\backslash (\backslash$$ $400\mathrm{.}00\backslash )$ was credited to the account on day $15.$ If the unpaid balance at the start of the billing cycle was $\backslash (\backslash$$ $1,622\mathrm{.}25\backslash ),$ show how much interest will be charged at the end of the billing cycle? What will the unpaid balance be at the start of the next billing cycle?

Use excel to answer the questions above. Your excel sheet should show the balance for each day and the formula used to calculate the balance for each day. It should also contain a cell showing the formula used to calculate the interest charged at the end of the billing cycle.

Hint: The interest at the end of the month should equal $\backslash (\backslash$$ $28\mathrm{.}49\backslash )$ after you round to the nearest cent.