Answer:
Instead of keeping a balance she would rather need to pay the remaining mortgage balance of $843.51
Explanation:
The first task here is to compute the monthly payment of the car loan using the formula below:
PMT=P(r/n)/1-(1+r/n)^(-nt)
P=loan amount= $27,000
r=interest rate=6 %
n=number of monthly payments in a year=12
t= duration of loan=4 years ( 48/12)
PMT=27000*(6%/12)/(1-(1+6%/12)^(-4*12)
PMT=27000*(6%/12)/(1-(1+6%/12)^(-48)
PMT=27000*(6%/12)/(1-(1.005)^-48
PMT=135 /(1-0.787098411 )
PMT=634.10
The balance of the loan after one year is the present value of the remaining 36 monthly payments as computed thus:
PV=monthly payment*(1-(1+r)^-n/r
monthly payment=634.10
r=monthly interest rate=6%/12=0.5%
n=number of monthly payments left=36
PV=634.10*(1-(1+0.5%)^-36/0.5%
PV=634.10*(1-0.835644919 )/0.5%
pv=$20,843.51
balance left after paying the loan=$20,000-$20,843.51 =-$843.51
