Christina's monthly payment is $583
Her total interest payment is $584
What does monthly compounding mean?
Monthly compounding means that the interest on the loan is computed every month, it shows the frequency of interest computation during the loan tenure.
In this case, the monthly payment can be determined using the present value formula of an ordinary annuity since the monthly payment would occur at the end of each month.
PV=PMT*(1-(1+r)^-N/r
PV=loan amount=cost of car-down payment
PV=$18,000-$4,000
PV=$14,000
PMT=monthly payment=unknown
r=monthly interest rate=3.8%/12=0.003166666666666670
N=number of monthly payments=25
$14,000=PMT*(1-(1+0.00316666666666667)^-25/0.003166666666666670
$14,000=PMT*(1-(1.00316666666666667)^-25/0.003166666666666670
$14,000=PMT*(1-0.924001500485879000)/0.003166666666666670
$14,000=PMT*0.075998499514121000/0.003166666666666670
PMT=$14,000/0.075998499514121000*0.003166666666666670
PMT=$583.34
PMT=$583( nearest dollar)
The total interest is the total 25 monthly payments minus the loan amount
total interest=( $583.34*25)-$14,000
total interest=$583.50
total interest=$584
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