Question

bill was going to purchase a new mountain bike with his credit card, which he thought had an apr of 13%. his plan was to keep his payments around $75 per month for 24 months. he then found out that his credit card actually had an apr of 17%. which of the following would not allow bill to purchase a bike while keeping the same monthly payment?
a. purchase a bike that costs less.
b. wait for the bike he wants to go on sale for a cheaper price.
c. purchase the bike in a part of town with a higher sales tax rate.
d. increase the number of months he wants to use to pay off the balance.

Explanation:

Analyze the financial scenario

Using the Annual Percentage Rate knowledge point
The interest rate (APR) on Bill's credit card increased from \(13\%\) to \(17\%\). This higher rate increases the interest charges, which raises his monthly payment if all other factors (purchase price and repayment term) remain the same. To keep his monthly payment at \(75\) dollars, Bill must offset this interest rate increase.

Evaluate options that reduce the total cost

Using the Sales Tax Calculation knowledge point

• Option a (Purchase a bike that costs less): Decreasing the purchase price reduces the principal balance, which lowers the monthly payment. This is a valid way to offset the higher APR.
• Option b (Wait for the bike to go on sale): A lower sale price also reduces the principal balance, lowering the monthly payment. This is a valid way to offset the higher APR.
• Option c (Purchase in a part of town with a higher sales tax rate): A higher sales tax rate increases the total purchase price (principal balance), which increases the monthly payment. This would make his monthly payment even higher, failing to keep it at \(75\) dollars.

Evaluate option that adjusts the repayment term

• Option d (Increase the number of months to pay off the balance): Spreading the payments over a longer period (more than \(24\) months) reduces the size of each monthly payment, which can offset the higher interest rate. This is a valid way to keep the monthly payment at \(75\) dollars.

Identify the correct choice

The question asks which option would not allow Bill to purchase a bike while keeping the same monthly payment. Option c increases his total cost and monthly payment, so it is the correct choice.

Answer:

• a. Purchase a bike that costs less.
• b. Wait for the bike he wants to go on sale for a cheaper price.
• c. Purchase the bike in a part of town with a higher sales tax rate. (Correct answer)
• d. Increase the number of months he wants to use to pay off the balance.