##### Need business and finance help to find the APR and Calculate the (EAR) effective Annual Rate

 Business & Finance Tutor: None Selected Time limit: 1 Day

Pick a credit Card or home or auto offer from the mail. Find the APR and Calculate from the (EAR) effective Annual Rate. Show the work

Dec 1st, 2015

Thank you for the opportunity to help you with your question!

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

i={(1+r/m)^m}−1

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%

Please let me know if you need any clarification. I'm always happy to answer your questions.
Dec 1st, 2015

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Dec 1st, 2015
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Dec 1st, 2015
Dec 11th, 2016
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