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Round to the nearest penny.

You owe $1,350.00 on a credit card with a 14.25% APR. You
pay $300.00 at the beginning of the month.
How much interest do you save by paying at the beginning
of the month versus at the end of the month?

Along the same lines as the question above. Imaginge you put the
$300 in a savings account earning 3.0% APR instead of using
it to pay down your credit card in the above problem. What
is the difference between the interet your savings account would
earn that month vs the interest that woujld accrue on your credit card that month
if you didn't use the $300 to pay it down?

1 answer

To solve these problems, we need to find out how much interest accrues on the credit card balance from both scenarios: paying down the balance at the beginning of the month versus at the end. After that, we will compare the interest from a savings account versus the interest accrued on the credit card.

Let's break this down step by step:

Part 1: Interest Savings from Paying at the Beginning vs the End of the Month

  1. Calculate Monthly Interest Rate:

    • The annual percentage rate (APR) is 14.25%.
    • Monthly interest rate = 14.25% / 12 = 1.1875%.

  2. Calculate Interest Accrued if the $300 is Paid at the Beginning of the Month:

    • The balance after the payment = $1,350.00 - $300.00 = $1,050.00.
    • Interest accrued on $1,050.00 for one month = $1,050.00 * 0.011875 = $12.49 (rounded to 2 decimal places).

  3. Calculate Interest Accrued if the $300 is Paid at the End of the Month:

    • The full balance of $1,350.00 incurs interest for one month.
    • Interest accrued on $1,350.00 for one month = $1,350.00 * 0.011875 = $16.13 (rounded to 2 decimal places).

  4. Calculate Interest Savings:

    • Savings = Interest if paid at the end - Interest if paid at the beginning.
    • Savings = $16.13 - $12.49 = $3.64.

Part 2: Interest Earned in Savings Account vs Interest on Credit Card

  1. Calculate Interest Earned in Savings Account if $300 is Deposited:

    • The interest from the savings account for one month at 3.0% APR:
    • Monthly interest rate for savings = 3.0% / 12 = 0.25% = 0.0025.
    • Interest earned on $300.00 = $300.00 * 0.0025 = $0.75.

  2. Calculate Interest Accrued on the Credit Card Without Paying Down:

    • This will be the same as the interest calculated before for the whole balance of $1,350.00:
    • Interest accrued = $1,350.00 * 0.011875 = $16.13 (already calculated).

  3. Calculate the Difference:

    • Difference = Interest accrued on credit card - Interest earned in savings.
    • Difference = $16.13 - $0.75 = $15.38.

Summary:

  • Interest Saved by Paying at the Beginning of the Month: $3.64
  • Difference between Interest on Credit Card and Interest Earned on Savings: $15.38

Thus, the final answers are:

  • Interest savings by paying at the beginning of the month vs. the end: $3.64
  • Difference between interest you would accrue vs. interest you would earn in savings: $15.38