Sasha wants to buy a new HDTV for $2769.00. He doesn't have the cash right now, so he decides to use credit. His credit card gives him a grace period of 15 days, then will charge him an annual interest rate of 16%, compounded daily, which is 0.04066% per day. The store offers him an annual interest rate of 15%, compounded daily (0.03829% per day), but with no grace period. If Sasha intends to pay off the debt 60 days from now, which payment plan should he use? Assume he doesn't make any payments for 60 days.
To buy the HDTV for $2769 Sasha has to borrow money. There are two options available for him. If he uses his credit card, he is given a grace period of 15 days following which interest is charged at 0.04066% per day compounded daily. If Sasha uses this option and makes a payment after 60 days the total amount due is 2769*(1+0.0004066)^(60 - 15) = $2820.12
The offer given by the store comes with an interest rate of 0.03829% per day compounded daily but no grace period. If this option is used the total amount due is 2769*(1+(0.0003829)^60 = $2833.34
As the amount payable after 60 days in the first option is smaller Sasha should use his credit card.