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 (1 mark) N = _______ I% = _______ PV = ________ PMT = ___________ FV = _________ P/Y = _________ C/Y = _______ b. New Card (1 mark) N = _______ I% = _______ PV = ________ PMT = ___________ FV = _________ P/Y = _________ C/Y = _______ c. Least expensive card
You have to use this online financial calculator to figure this out:
https://arachnoid.com/finance/
1- You have to convert the interest rate from compounded daily to compounded monthly, because the payments are made monthly and the interest rate must match the monthly payments. So:
15.9% compounded daily =16% compounded monthly.
PV =$4,785.00, monthly payments =$350.00, payments per year(P/Y)= 12, compounding periods per year(C/Y) =12, FV of the loan =$5,851.86, number of monthly payment(N) =15.19 months.
Total cost of principal + interest =15.19 months x $350.00 =$5,317.84
2- Do exactly the same for the 2nd card:
14.2% compounded daily = 14.28% compounded monthly.
PV =$4,785.00, monthly payments =$350.00, payments per year(P/Y) = 12, compounding periods per year(C/Y) = 12, FV of the loan =$5,714.85, mumber of monthly payments(N)= 15.01 months.
Total cost of principal + interest =15.01 months x $350 =$5,253.45
3- Total cost on the 1st card =$5,317.84 - [2% x $4,785.00] =$5,222.14 Net cost on 1st card.
Total cost on the 2nd card =$5,253.45 - $100 = $5,153.45 Net cost on 2nd card.
$5,222.14 - $5,153.45 = $68.69 - difference in net cost between card 1 and card 2
Therefore, the second card is a bit cheaper, or $68.69 cheaper!.
Note: Compounding periods of 365 days per year on both cards = 12 compounding periods per year after both interest rates are converted to monthly compound. That is: 15.9% and 14.2% componded daily are EQUIVALENT to 16% and 14.28% compounded monthly.
