Question

Darcy is buying a new couch that cost $999.00. She has two payment options.

Option 1: Pay with credit card. The card charges 20.00% annual interest and Darcy expects to pay off the charge in 30 days.

Option 2: Take the store promotion of 15 monthly payments of $70 (including tax)

a) Calculate the total cost of each option
b) What is the annual interest rate being charged with Option 2?

Please show your work. ​​

Answer 1

Step-by-step explanation: a) To calculate the total cost of the couch when paid with a credit card, we need to calculate the amount of interest that will be charged. To do this, we first need to calculate the monthly interest rate by dividing the annual interest rate by 12. In this case, the monthly interest rate is 20/12 = 1.67%.

Next, we need to multiply the cost of the couch by the monthly interest rate to find the amount of interest that will be charged. In this case, the amount of interest is 999 * 1.67% = 16.67.

Finally, we need to add the amount of interest to the cost of the couch to find the total cost when paid with a credit card. In this case, the total cost is 999 + 16.67 = 1015.67.

To calculate the total cost of the couch when paid with the store promotion, we simply need to add up all 15 monthly payments. In this case, the total cost is 15 * 70 = 1050.00.

b) To calculate the annual interest rate being charged with Option 2, we need to divide the total cost of the couch by the number of monthly payments and then multiply by 12. In this case, the annual interest rate is (1050/15)*12 = 96%.