You decide to treat yourself with a set of new wheels. The car you want costs about $56,000, and you can afford a $10,000 down payment. The bank quotes an interest rate of 15 percent APR for a 6-year loan for the amount outstanding. What will your monthly payment be? What is the effective interest rate on the loan?

 

a.

To start with, the car loan amount is the cost of the car minus the down payment of $10,000.

Car loan amount=$56,000-$10,000=$46,000

Annual percentage Rate(APR)=15%

monthly interest rate=15%/12= 1.25%

number of monthly payments in 6 years=12*6=72

The applicable formula is the present value of an ordinary stated below:

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

PV=loan amount=$46,000

r=monthly interest rate=1.25%

n=72 months

46000=monthly payment*(1-(1+1.25%)^-72/1.25%

46000=monthly payment*(1-(1.0125)^-72/0.0125

46000=monthly payment*(1-0.4088441)/0.0125

46000=monthly payment* 0.5911559/0.0125

monthly payment=46000*0.0125/0.5911559= $972.67 

b.

Effective interest rate=(1+APR/n)^n-1

APR=15%

n=number of times that interest is compounded annually=12 ( since it is monthly repayment loan)

Effective interest rate=(1+15%/12)^12-1= 16.08%