interest compounded more frequently

| June 3, 2016

Question
You are considering buying a home. The agreed upon price is $200,000. You decide to put down $20,000. Your bank agrees to finance the difference at 4% APR, for 30 years. The mortgage must be paid monthly.

A) Calculate your monthly mortgage payment. (Hint: Notice that the formula used to calculate this amount is similar to that of an annuity, with interest compounded more frequently than a year.)

B) Calculate the portion of your interests to be paid the first month. (Hint: To calculate this amount, one should use the simple interest on the “new” balance each period)

C) Calculate the portion of your principal to be repaid the first month.

D) Calculate the total amount you will end paying after 30 years, assuming nothing change during this term.

E) Construct an amortization table for the first three years of this mortgage.

F) Supposed that the appraised value of the house you are purchasing is $205,000. What is your Loan-to-Value ratio?

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