Listed below are the balances and annual percentage rates for Jimmy's credit cards. If Jimmy makes the same payment each month t
o pay off his entire credit card debt in the next 12 months, how much will he have paid in interest in the 12 month period?(Hint, find out how much interest Jimmy pays to each card over the 12 months seperately, and then add them together.) Credit Card Current Balance APR A $563.00 16% B $2,525.00 21% C $972.00 19% a. $321.83 b. $370.75 c. $449.24 d. $730.80 c
Hi there We know that the formula of the present value of annuity ordinary is Pv=pmt [(1-(1+r/k)^(-kn))÷(r/k)] Pv present value PMT monthly payment R interest rate K compounded monthly 12 because the payment is monthly N time What we need from the formula above to find the monthly payment So to find the monthly payment the formula PMT=pv÷[(1-(1+r/k)^(-kn))÷(r/k)] Another important things we need is how to find total payments and interest charge To find total payments Monthly payment×12 And to find interest charge Total payments-present value
Now let's find interest charge for each credit card Credit card A The monthly payment is PMT=563÷((1−(1+0.16÷12)^( −12))÷(0.16÷12))=51.08 Total payments 51.08×12=612.96 interest charge 612.96−563=49.96
Credit card b PMT=2,525÷((1−(1+0.21÷12)^( −12))÷(0.21÷12))=235.11 Total payments 235.11×12=2,821.32 interest charge 2,821.32−2,525=296.32
Credit card c PMT=972÷((1−(1+0.19÷12)^( −12))÷(0.19÷12))=89.58 Total payments 89.58×12=1,074.96 interest charge 1,074.96−972=102.96
So total interest charge for all credit cards is 102.96+296.32+49.96 =449.24....final answer