Question

Calculate the APR of a loan for $9.925, including loan fees of $270, at 12.5% for 6 years. (Do not round intermediate calculations. Round your answer to the nearest tenth percent.) APR

Answer 1

First, we will find the monthly payment,pmt. on the loan

whoes present value ,PV = $ 9925

at the given interest rate of r= 12.5%/12= 1.0417% p.m. or 0.010417

for a period of n= 6yrs.*12= 72 months

using the PV of ordinary annuity formula,

PV of loan=pmt.*(1-(1+r)^-n)/r

Substituting the values in the above formula,

9925=pmt.*(1-(1+0.010417)^-72)/0.010417

the mthly.pmt.=9925/((1-(1+0.010417)^-72)/0.010417)=

196.63

Now, with this above mthly.pmt. Of $ 196.63

we will find the r, which will equate the PV to 9925-270= $ 9655

(the net cash amt. after paying the loan fees)

Using the same formula,

9655=196.63*(1-(1+r)^-72)/r

Solving for r,we get r=

1.1292%

Now,this is the monthly r

To convert to APR

APR=(1+Mthly Rate)^12-1

ie.(1+1.1292%)^12-1=

14.42%

ANSWER: APR= 14.4%