here is teresas credit card statement for the month of january. (a) use the credit card statement to help…

here is teresas credit card statement for the month of january. (a) use the credit card statement to help fill in the table below. note that there are 31 days in january. also, a purchase increases the unpaid balance, and a payment decreases the unpaid balance. date transaction january 1 beginning balance $2280.10 january 7 purchase $700.50 january 14 payment $352.00 january 20 purchase $840.46 date transaction january 1 beginning balance $2280.10 january 7 purchase $700.50 january 14 payment $352.00 january 20 purchase $840.46 unpaid balance $2280.10 $2980.60 $ number of days at that balance 6 days (from january 1 through january 6) days (from january 7 through january 13) 6 days (from january 14 through january 19) 12 days (from january 20 through january 31) unpaid balance × number of days $13,680.60 total: $ total: 31 days (b) find the average daily balance. write your answer to the nearest cent. (c) suppose the credit card company charges an interest rate of 1.6% on the average daily balance for january found in part (b). how much interest will be charged? write your answer to the nearest cent. (d) what will teresas beginning balance be for the month of february (including the interest for january found in part (c))?

here is teresas credit card statement for the month of january. (a) use the credit card statement to help fill in the table below. note that there are 31 days in january. also, a purchase increases the unpaid balance, and a payment decreases the unpaid balance. date transaction january 1 beginning balance $2280.10 january 7 purchase $700.50 january 14 payment $352.00 january 20 purchase $840.46 date transaction january 1 beginning balance $2280.10 january 7 purchase $700.50 january 14 payment $352.00 january 20 purchase $840.46 unpaid balance $2280.10 $2980.60 $ number of days at that balance 6 days (from january 1 through january 6) days (from january 7 through january 13) 6 days (from january 14 through january 19) 12 days (from january 20 through january 31) unpaid balance × number of days $13,680.60 total: $ total: 31 days (b) find the average daily balance. write your answer to the nearest cent. (c) suppose the credit card company charges an interest rate of 1.6% on the average daily balance for january found in part (b). how much interest will be charged? write your answer to the nearest cent. (d) what will teresas beginning balance be for the month of february (including the interest for january found in part (c))?

Answer

Explanation:

Step1: Calculate unpaid balances for each period

From January 1 - 6: Unpaid balance = $2280.10$ From January 7 - 13: Unpaid balance = $2280.10 + 700.50=2980.60$ From January 14 - 19: Unpaid balance = $2980.60 - 352.00 = 2628.60$ From January 20 - 31: Unpaid balance = $2628.60+840.46 = 3469.06$

Step2: Calculate weighted - balances for each period

For January 1 - 6 (6 days): Weighted - balance = $2280.10\times6 = 13680.60$ For January 7 - 13 (7 days): Weighted - balance = $2980.60\times7=20864.20$ For January 14 - 19 (6 days): Weighted - balance = $2628.60\times6 = 15771.60$ For January 20 - 31 (12 days): Weighted - balance = $3469.06\times12=41628.72$

Step3: Calculate the sum of weighted - balances

Sum of weighted - balances = $13680.60 + 20864.20+15771.60 + 41628.72=91945.12$

Step4: Calculate the average daily balance

Average daily balance=$\frac{91945.12}{31}\approx2965.97$

Step5: Calculate the interest

Interest = $0.016\times2965.97\approx47.46$

Step6: Calculate the beginning balance for February

Beginning balance for February = Average daily balance+Interest = $2965.97+47.46 = 3013.43$

Answer:

(a) Unpaid balance from January 7 - 13: $2980.60$; Unpaid balance from January 14 - 19: $2628.60$; Unpaid balance from January 20 - 31: $3469.06$ (b) Average daily balance: $$2965.97$ (c) Interest: $$47.46$ (d) Beginning balance for February: $$3013.43$