Round all of your answers to the nearest cent when appropriate to do so. Some questions are programmed to allow for slight variations in the answers due to rounding errors, BUT it is important that you don't round values you are using in formulas. Only round your final answers. In this lab, you will be computing various values associated with paying off a balance on a credit card. Imagine the following scenario: You have received your monthly credit card statement and must now deal with the financial realities of last month's birthday celebration. While your birthday was deserving of a celebration, dealing with the $1700 in credit card charges will require some planning. Your credit card statement lists the APR (Annual Percentage Rate) for your balance to be 14.4%. This is the yearly interest rate the credit card company uses in calculating interest due on your balance. Express the APR as a decimal: (Note: For this lab,round your monthly interest rate to 5 decimal places. Using more decimal places of accuracy would result in minor changes to your answers, but just by a few cents.) i=12APR The minimum payment required by your credit card company is $25 per month. Assuming that you do not make any new charges to your account, you will answer the following questions to help you determine the best plan for paying off this credit card debt. a) To begin with, let's check out the plan of only paying the minimum amount due each month. To get a feel for how this will affect the balance, you'll compute the interest and the balance on the first few months assuming a the minimum monthly payment of $25. Let Bk represent the balance for the kth month and Ik represent the interest charged for the kth month. For example, I1 is the interest charged on the original balance and B1 is the original balance plus I1 minus the $25 payment (said differently, B1 is the balance after one month). Start by finding those values. For this exercise, round all values to the nearest cent (2 decimal places). (Hint: Ik=iBk1 ) I1=$B1=$ Now use B1 to find the interest charged for the 2nd month which is I2, and the balance after 2 months, which is B2 (don't forget to subtract the $25 payment). I2=$B2=$ Got it? Ok, you're ready to figure out how much interest you will be charged for the rest of the year and what your final balance will be after 12 months of just making the minimum payment. Finish filling in the following "table". I3=$I4=$I5=$I6=$I7=$I4=$B5=$B6=$B7=$B8=$ I9=$B9=$I10=$B10=$I11=$B11=$I12=$B12=$ b) How much of the original balance has been paid off at the end of the first year? Answer: \$ c) What is the total amount that has been paid to the credit card company at the end of the first year? (this is just your minimum payment per month times 12 months.) Answer: \& d) What percentage of what you paid went to paying the interest? Express your answer as a percentage and round it to one decimal place. Answer: % Warning! You must answer all of the questions in order for the lab to function properly. You can submit answers one at a time (or multiple at a time) so that you can make sure it is correct before proceeding to the next. Part II A formula for calculating the payment, P, required to pay off a debt of amount D in M months with monthly interest rate i is P=1(1+i)MDi a) Using this formula, solve for M. Use either the Common log, log, or the Natural log, ln. Starting with " M= ", enter the whole formula. Note: Use an asterisk () between any variables that are being multiplied together. For example, Di. If you need to, look back to Question 1 to recall the debt amount. D=$ b) Determine the number of months it will take to pay off the credit card debt with minimum monthly payments of $25. You'll need the monthly interest rate from Part I: i=0.012. Round the number of months to two decimal places. Number of months: c) How long is this in years, rounded to the nearest tenth of a year? Answer: d) What is the total amount paid to the credit card company, rounded to the nearest dollar? (Hint: Multiply the payment amount with your answer to part b)). Total Amount:\$ e) How much of the total paid goes toward interest? Interest:4 Warning! You must answer all of the questions in order for the lab to function properly. You can submit answers one at a time (or multiple at a time) so that you can make sure it is correct before proceeding to the next. Part III Using the formula for M from question 2, answer the following questions: a) Determine the number of months it will take to pay off the $1700 credit card debt with a monthly payment of $50. Round the number of months to two decimal places. Number of months: b) How long is this in years, rounded to the nearest tenth of a year? Answer: c) What is the total amount paid to the credit card company, rounded to the nearest dollar? (Hint: Multiply the payment amount with your answer to part a)) Total Amount: \$ d) How much of the total paid goes toward interest? Interest: \$ Using the formula for M from question 2, answer the following questions: a) Determine the number of months it will take to pay off the $1700 credit card debt with a monthly payment of $75. Round the number of months to two decimal places. Number of months: b) How long is this in years, rounded to the nearest tenth of a year? Answer: c) What is the total amount paid to the credit card company, rounded to the nearest dollar? (Hint: Multiply the payment amount with your answer to part a)) Total Amount: \& d) How much of the total paid goes toward interest? Interest: \$ a) Using the formula for calculating the payment, P, determine how large of a payment is required to pay off a debt in 12 months. Use the same monthly interest rate i=0.012 and the same debt amount $1700 from the first question. The formula you need is: P=1(1+i)MDi P=$ b) What is the total amount paid to the credit card company? (Hint: Multiply the payment amount by 12). Total amount: \$ c) How much of the total paid goes toward interest? Interest: \$