a. Suppose Jose spontaneously decides to treat all his friends to pizza, drinks, and dessert at a dine-in Italian place. He has already spent his excess cash from his paycheck so he decides to put it on his credit card and pay for it later. The total cost for the pizza for his group of friends including the tip is $125.87. His credit card has an interest rate of 20.99%. If he makes payments of $30 per month, how long it take him to pay for that spontaneous purchase

It takes him approximately 5 months (5.08 months) to pay for the spontaneous purchase.

Explanation:

First of all, let us lay out the important information contained in the question clearly:

total cost of purchase = $125.87

interest rate = 20.99% (0.2099)

repayment plan = $30 per month.

Next you have to calculate the total amount incurred on the credit card after interest have been added, and this is calculated as:

total incurred amount = interest on amount + initial amount

To calculate interest on the original, amount, we will convert the interest rate to amount, and this is shown below:

interest on amount = interest rate * original amount

= 0.2099 * 125.87 = 26.420113

Therefore, total incurred amount = 26.4201 + 125.87 = $152.2901

Finally, we are told that Jose has a repayment plan of $30 per month, so, at this repayment rate, we will find how long it will take for him to complete the payment, as shown:

Number of months to make complete payment = total amount : payments per month

Number of months to make complete payment = 152.2901 : 30 = 5.08 months = 5 months approximately.