Question

You take out a mortgage loan from First Bank of Terlingua with the following characteristics:

• compounding period is monthly

• loan is for $200,000

• APR = 6.17%

• initial maturity is 30 years

• this mortgage loan has no points

Now suppose that First Bank allows you to accelerate your loan payments by paying an additional $100 each month. (We assume that the bank does not charge a fee for exercising this option.) When we take the acceleration into account, what is your effective annual rate?

Answer 1

Since the capital is compounding period is monthly, the total periods in a year will be 12.

Annual Percentage Rate (APR) = Periodic rate * Number of periods in a year

or, 6.17 = Periodic rate * 12

So, Periodic rate = 6.17/12 = 0.5142 % compounded monthly

Now, Effective annual rate = (1 + periodic rate%)^{Number of periods} - 1

= (1 + 0.5142%)¹² - 1 = (1 + 0.005142)¹² - 1 = 1.005142¹² - 1 = 1.06348 - 1

= 0.06348 ~ 6.348

Hence, the effective annual rate is 6.348.