You are considering 2 means of financing a spring break vacation. You can put it on your credit card, at 16% APR, compounded monthly, or borrow the money from your paleas, that want an interest payment of 7% eexceptionally six months.

You watching: You are considering two ways of financing a spring break vacation

Which is the reduced rate? (Note: Be mindful not to round any kind of intermediate procedures less than six decimal places.)

The efficient yearly price for your credit card is ....................................... (Round to two decimal locations.)

## Effective Annual Rate:

The efficient yearly rate is a calculation process that presents the results of compounding in an investment. By computing the reliable yearly price of various investments, investors can estimate the project"s viability by choosing the highest (investor) or lowest (borrower) rate.

We have to compute the reliable annual price of each choice. For this, we have to identify the APR of each option. We recognize that the APR of the credit card is 16%, compounded monthly. On the various other hand, we deserve to compute the APR of the parent"s alternative by multiplying 7% and 2. Thus, the APR of the parent"s alternative is 14% compounded semiyearly (every six months.)

EAR equation:

eqEAR=(1+dfracrm)^m-1/eq

Wright here,

**EAR**= efficient annual rate

**r**=interemainder price (in decimal form)

**m**= variety of compounding periods.

Credit card:

r= 0.16; m= 12 (compounded monthly)

eqEAR=(1+dfrac0.1612)^12-1 = 0.1722707983 = 17.23\%/eq

Parent"s option:

r= 0.14; m= 2 (compounded semiannually)

eqEAR=(1+dfrac0.142)^2-1 = 0.1449 = 14.49\%/eq

As such, the lowest interest is the parent"s option.

The EAR of the credit card is 17.23%.

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Effective Annual Rate: Formula & Calculations

from

Chapter 7/ Lesson 611K

After watching this video lesson, you will understand just how the interest price that financial establishments, such as crmodify card carriers, offer you work-related. Also, learn just how this interest price might be different than the one you actually finish up via.

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