Davis owns a moving business and one of his trucks needs a new transmission along with some other repairs that will cost a total of $4785. He can use his credit card with an annual rate of 15.9% compounded daily that offers 2% cash back on all purchases made on the card or he can sign up for with a new card company that is offering a $100 rebate the first time the card is used. This card has an annual rate of 14.2% compounded daily. Which card would be less expensive and by how much less if he can afford to pay back $350 per month? Both the cash back and rebate are a cheque sent in the mail. They do not affect any of your inputs for part (a) or (b), only in part (c). (use your financial application and fill in the appropriate inputs)
a. Existing Card
b. New Card
C. Least Expensive Card
First, you have to convert both interest rates from compounded daily to compounded monthly:
15.9% = 16.00% compounded monthly.
14.20%=14.28% compounded monthly.
Then you would have to use this formula to calculate the monthly payment or the number of months required to pay off the loan: PMT=PV. R.{[1 + R]^N/ [1 + R]^N - 1}
Unfortunately, there is no direct solution for N, or number of months, at least not an easy one!. See the note below. However, if you have a financial calculator and enter all the variables in, you should get N =15.19 months on the first card @ 15.9%.
[15.19 x $350] - $4,785 =$531.50 Total interest on the 15.9% card.
And N =15.01 months on the second card @ 14.2%
[15.01 x $350] - $4,785 =$468.5 Total interest on the 14.2% card.
You can subtract the bottom from the top to get the difference.
@2% on $4,785 =$95.70 Check he will get in the mail on the 15.9% card.
And $100 he will get on opening a new account on the second card @ 14.2%
$531.50 - $95.70 =$435.80 Net cost on the first card @ 15.9%
$468.50 - $100 =$368.50 Net cost on the second card @ 14.2%.
Now, you can see the net difference by subtracting one from the other.
Note: There is a relatively involved formula for finding N, or the number of months, and it looks like this: N =Log[(-FV*R+PMT) /(R*PV+PMT) ] / Log[R+1]
