A year after buying her car, Anita has been offered a job in Europe. Her car loan is for $27,000 at a 6% nominal interest rate for 48 months. If she can sell the car for $20,000, how much does she get to keep after paying off the loan

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