Question

Guzman just borrowed $79,000 to buy a filtrstion system. The terms of the loan require him to make equal regular quarterly payments for 8 years plus an extra payment of $ 5,500 in 8 years. His first regular quarterly payment is due in 3 months. If guzmans regular quarterly payment is &3,656.12 , then what is the EAR of his loan.

a 11.16% ( plus or minus .03 percentage points)

b 13.01% ( plus or minus .03 percentage point

c 11.64 % ( plus or minus .03 percentage point

d 10.72 % ( plus or minus .03 percentage point

e none

Answer 1

= C*[1-(1+i)^-n]/i] +final amount/(1+r)^32
Where,
C= Cash Flow per period
i = interest rate per period
n=number of period c=8*4 =32
79000= $3656.12[ 1-(1+r)^-32 /r] +5500/(1+r)^32
79000/3656.12 =[ 1-(1+r)^-32 /r] +5500/(1+r)^32
2.16076 =[ 1-(1+r)^-32 /r] +5500/(1+r)^32
r = 2.79%
Effective Annual Rate = (1+0.0279)^ 4 -1
=11.64%
Correct Answer =c 11.64 % ( plus or minus .03 percentage point