Nate would like to buy a camper for his truck at a cost of $5250. He has two financing options. The dealership offers financing at an annual rate of 15.5% compounded monthly with $350 worth of free upgrades for the camper. His credit card has zero balance and has an annual rate of 13.3% compounded daily. He plans to pay off the debt in one year.
Which option will charge less interest and how much is that interest?
The first thing you have to do is to convert the interest rate of 13.3% from compounded daily to compounded monthly:
13.3% compounded daily =13.3715276596% compounded monthly.
Then you have to use this formula to calculate the monthly payments in each case:
PMT=PV. R.{[1 + R]^N/ [1 + R]^N - 1}
PMT =$475.10 - This is the monthly payment @15.5% loan of $5250 from the dealership.
$475.10 x 12 - $5,250 =$451.20 Interest on the loan from the dealership.
PMT =$469.83 - This is the monthly payment @13.37% loan of $5,250 from the credit card.
$469.83 x 12 - $5,250 =$387.96 Interest on the loan from credit card.
Now, you can see the difference in total interest. You have to determine whether Nate will get the $350 free upgrades whether he borrows the money from the dealership or puts it on his credit card. If it is conditional on borrowing the money from the dealership, then the loan from the dealership would be much cheaper. Otherwise, the credit card would be cheaper.
