Question

g Find the monthly payment and estimate the remaining balance (to the nearest dollar). Assume interest is on the unpaid balance. 5-year car loan for $9700 at 5%; remaining balance after 4 years.

Answer 1

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