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

*label*Business Finance

*timer*Asked: Dec 1st, 2015

*account_balance_wallet*$5

### Question Description

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

## Tutor Answer

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.

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