Answer:
Monthly payment $102.88
Outstanding balance after year 4 $1,201.76
Explanation:
First and foremost, the car loan amount of $9,700 is the present value of all monthly payments for 5 years as shown below:
PV=monthly payment*(1-(1+r)^-n/r
PV=car loan amount=$9,700
monthly payment=unknown
r=monthly interest rate=5%/12=0.004166667
n=number of monthly payments in 5 years=5*12=60
$9700=monthly payment*(1-(1+0.004166667)^-120/0.004166667
$9700=monthly payment*(1-(1.004166667)^-120/0.004166667
$9700=monthly payment*(1-0.607161016
)/0.004166667
$9700=monthly payment*0.392838984
/0.004166667
$9700=monthly payment*94.28134862
monthly payment=$9700/94.28134862
monthly payment=$102.88
The outstanding balance after year 4 is the present value of monthly payments for the remaining 1 year(12 months)
PV=$102.88*(1-(1+0.004166667)^-12/0.004166667
PV=$102.88*(1-(1.004166667)^-12/0.004166667
PV=$102.88*(1-0.951328238
)/0.004166667
PV=$102.88*0.048671762
/0.004166667
PV=$1,201.76
