Question

Ann gets a fully amortizing 30-year fixed rate mortgage with quarterly payments for $1,000,000. The interest rate is 4%, compounded quarterly. She prepays the mortgage in 1 quarter (i.e. she makes the 1st payment and immediately prepays the remaining balance).

There is still an origination fee of 2 points, but now Ann decides to keep the mortgage for the whole term, i.e. she no longer plans to prepay it. What is Ann’s APR?

Answer 1

ANSWER

Since interest rate for the loan at 4% is compounded quarterly, APR, in the absence of any closing costs, is 4% itself, when paid off in one quarter as follows:

Principal (P)= $1,000,000

Interest rate (R )= 4%

Period (N) = ¼ year

Interest for the first quarter= PRN

= 1,000,000*4%/4 = $10,000

Interest rate= (10000/1000000)*4*100 = 4%

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