Question

A couple takes out a fully amortizing fixed rate thirty-year loan for $375,000. The couple makes monthly payments and the annual interest rate on the loan is 4.5%. The couple also pays 3 points in up- front fees to obtain the loan. (a) Calculate the loan’s APR [8 points] (b) Assuming a holding period of 12 years, calculate the loan’s EBC

Answer 1

Sol:

Loan amount = $375,000

Interest rate (r) = 4.5% (Monthly payment) = 4.5%/12 = 0.3745%

Period (n) = 30 years (Monthly) = 30 x 12 = 360

Fees for loan = 3% of $375,000 = $11,250

PMT = PV/ ((1-(1/(1+r)^n))/r)

PMT = 375000/ [(1-(1/(1+0.375%)^360))/0.375%]

PMT = 375000/ [(1-(1/(1.00375)^360))/0.00375]

PMT = 1900

Now total interest paid over 30 years = (1900 x 360) - 375000 = 309000

APR = ((Interest + fees ) / (n x Principal) x 12

APR = (309000 + 11250)/(30 x 375000 )

APR = 0.028467 or 2.85%

b) Assuming holding period of 12 years, loan’s EBC wil be as follows.

PMT = 375000/ ((1-(1/(1+0.375%)^144))/0.375%) = 3375

Total interest paid = (3375 x 144) - 375000 = 111000

Total finance cost (f) = 111000+11250 = 122250

Total amount paid (a) = 3375 x 144 = 486000

EBC = 2 x (f x 12) / (a x (n+1))

EBC = 2(122250 x 12)/(486000 x 145)

EBC = 2(1467000 / 70470000)

EBC = 0.0416 or 4.16%

Therefore APR will be 2.85% and EBC will be 4.16%