Question

Suppose you have an outstanding balance of $400 on your credit card, which has a 15%

APR. You have carefully considered your budget and decided that you can afford to pay
$75 per month until the balance is paid in full. You have also decided that you will not
make any additional purchases using the card.
4
Assuming that the card compounds daily, what will the balance be after the first payment
at the end of the first month?

Answer 1

The first step is to calculate the daily interest rate. We can do this by dividing the annual percentage rate (APR) by 365 (the number of days in a year):

Daily interest rate = 15% / 365 = 0.00041096

Next, we need to calculate the interest that accrues on the outstanding balance for the first month. Since there are 30 days in a typical month, we can multiply the daily interest rate by the outstanding balance and the number of days in the month:

Interest for first month = 0.00041096 × $400 × 30 = $4.93

This means that the outstanding balance after the first payment will be:

$400 + $4.93 - $75 = $329.93

So the balance after the first payment will be $329.93.