cash diagram and calculating

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Many credit cards offer an initial grace period; if you pay off your balance during that period you don’t accrue any interest (though some credit cards have no grace period with interest accruing immediately). Each credit card also has their own calculation for the minimum payment you are required to make each billing period. It’s typically between 2%-5% of the 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 15% – 23% with daily compounding.

You’ve signed up for a new credit card from BrooksBank. BrooksBank charges 18.5% per year with daily compounding for any balance not repaid within the grace period, and the required minimum payment is calculated as 3% of the outstanding balance. With your new card, you decided to upsize your television, and have purchased an 82” Samsung LED TV for $1,988.00. (Links to an external site.) (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) Multiplying the purchase price ($1,988.00) by the annual interest rate (18.5%) gives me $367.78. Is that the amount of interest you will owe if you don’t repay the balance before the end of the first year?

For the last three parts of this problem, assume you make only the minimum required payment each month. (there is not a single simple formula to solve these, you’ll likely need to determine the balance and minimum payment for each month)

e) One year after you purchased the TV, what is your credit card balance?

f) One year after you purchased the TV how much interest have you accrued over the year?

g) Add the monthly payments you’ve made (the cash you’ve actually spent) plus the credit card balance after one year (the amount you still owe) and compare that to the initial purchase price. Explain why these numbers are similar or different from one another.

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