Some credit cards offer an initial grace period, if you pay off your balance during that period

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Question:

Some credit cards offer an initial grace period, if you pay off your balance during that period you don’t accrue any interest. Other credit cards have no grace period with interest accruing immediately. Each credit card also has their own calculation for determining the minimum payment you are required to make each billing period. It’s typically between 2%-5% of the balance or $20-$25 (whichever is larger; not to exceed the entire credit card balance), but, it may also include fees or finance charges. Since each card is different, you have to check the terms of the credit card agreement to be certain of the details. Interest rates on credit cards range widely, current annual rates fall between 13% - 25% with daily compounding.

You’ve signed up for a new credit card from AlbrightsonBank. AlbrightsonBank charges 19.5% per year with daily compounding for all outstanding balances. There is no grace period, so interest accrues immediately upon purchase. The required minimum payment is calculated as the largest of the following:

2.0% of the outstanding balance
$20.00, if your balance is greater than $20.00
Your entire outstanding balance, if your balance is less than $20.00

With your new card, you decided to upsize your television, and have purchased an 85” Samsung TV for $1,897.99 (Links to an external site.) since that price is about 20% lower than you've seen for comparable TVs. For this problem, assume that interest begins to accrue from the initial purchase date, the first payment is due exactly one month after the purchase date of the TV, with additional payments due each month thereafter.

a) What is the nominal rate for this credit card?

b) What is the effective annual rate for this credit card?

c) Why are they different?

d) One year after you purchased the TV, what is your credit card balance and what's the total of the payments you've made? Adding these together (what you still owe, plus what you've already paid), how does the total compare to the original purchase price?

e) Three years after you purchased the TV, what is your credit card balance and what's the total of the payments you've made? Adding these together (what you still owe, plus what you've already paid), how does the total compare to the original purchase price?

f) What does this tell you about the deal you got (20% off) on this TV and the use of credit cards?