7.84 Some lenders charge an up-front fee on a loan, which is subtracted from wha

Question

7.84

Some lenders charge an up-front fee on a loan, which is subtracted from what the borrower receives. This is typically described as "points" (where one point equals 1pecentage of the loan amount). The federal govern­ment requires that this be accounted for in the APR that discloses the loan's cost. A 5-year auto loan for dollar18,000 has monthly payments at a 9pecentage nominal annual rate. If the borrower must pay a loan origination fee of 2 dollar points, what is the true effective cost of the loan? What would the APR be? If the car is sold after 2 years and the loan is paid off, what is the effective interest rate and the APR? Graph the effective interest rate as the time to sell the care and pay off the loan varies from 1 to 5 years.

Explanation / Answer

a)First find monthly payment of the loan
=pmt(rate,nper,pv,fv,type)
rate=9%/12
nper=5*12=60
loan orgination fee=2%*18,000=$360
pv=18,000
Actual loan=18,000-360=$17,640
Fv=
type=0

PMT(9%/12,60,18000,,0)=$373.65

true effective cost
=RATE(60,-373.65,17640,,0,)=.82%
APR-0.82%*12=9.87%

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