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Since numbers are not given, taking own examples.
Average Percentage Rate:
The Alpha Mortgage loan in the example above carries the lower APR. With the Beta Mortgage loan, you’re essentially paying $3,000 for the privilege of borrowing $100,000, and thus effectively borrowing only $97,000. However, you’re still making interest payments that the lender is basing on a $100,000 loan, not a $97,000 one. A lower denominator has the same effect as a higher numerator. The APR on the Alpha Mortgage loan is 5.00%, but the APR on the Beta Mortgage loan is 5.02%.
To calculate the APR for a loan that incorporates costs beyond those of the principal borrowed, first determine how much the periodic payments are. For the Beta Mortgage loan, each monthly payment is $521.65 (formula)
The $100,000 is the gross principal borrowed, .0475 the interest rate, 12 the number of periods in a year, and 360 the number of periods over the course of the loan. Break out your calculator, and you’ll find that the monthly payment is $521.65.
Then, divide the monthly payment into the net amount you’re borrowing,
$521.65/$97000 = 0.0053 =5.3%
Effective Annual Rate Formula
Where r = R/100 and i = I/100; r and i are interest rates in decimal form. m is the number of compounding periods per year. The effective annual rate is the actual interest rate for a year.
Suppose you are comparing loans from 2 companies. The first offers you 7.24% compounded quarterly while the second offers you a lower rate of 7.18% but compounds interest weekly. Without considering any other fees at this time, which is the better terms? Using the effective annual rate calculator you can find the following.
At 7.24% compounded 4 times per year the effective annual rate calculated is
i = (1 + r/m)m - 1 = (1 + 0.0724/4)^4 - 1 = 0.07439 or I = 7.4389%
At 7.18% compounded 52 times per year the effective annual rate calculated is
i = (1 + r/m)m - 1 = (1 + 0.0718/52)^52 - 1 = 0.07439 or I = 7.4387%
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