Question

Mrs. Smith has saved $2,500 toward a new car and believes that she can afford monthly payments of $250.

1) If her bank offers financing terms of 60 months at a nominal 12% interest, what is the most she can pay for a car?

2) The dealer offers 9% financing but the loan is for only 36 months. What is the most she can pay for a car on this basis?

Please Show Solutions/Factors

Answer 1

Initial Saving =$2500

Monthly Payment =$250

r = 12%

monthly r = 12%/12=1%

n=60 months

We need to calculate the PV of the monthly payments

PV = P*(1-(1+r)^-n)/r

= 250*(1-(1+1%)^-60)/1%

=250*(1-(1.01)^-60)/0.01

=250*(1-0.55045)/0.01

=250*(0.44955)/0.01 (Factor = 44.955)

=$11238.76

Hence maximum payment for car = 2500+ 11238.76 = $13738.76

If, r = 9%

monthly r = 9%/12=0.75%

n=36 months

We need to calculate the PV of the monthly payments

PV = P*(1-(1+r)^-n)/r

= 250*(1-(1+0.75%)^-36)/0.75%

=250*(1-(1.0075)^-36)/0.0075

=250*(1-0.76415)/0.0075

=250*(0.23585)/0.0075 (Factor = 31.447)

=$7861.70

Hence maximum payment for car = 2500+ 7861.70 = $10361.70