Question

# Ann gets a fully amortizing 30-year fixed rate mortgage with quarterly payments for \$1,000,000. The interest...

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?

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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DEAR STUDENT,

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