You are considering the purchase of new living room furniture that costs $1,520. The store will allow you to make weekly payments of $32.33 for one year to pay off the loan. What is the EAR of this arrangment?

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Business

Alani

28 March, 04:48

You are considering the purchase of new living room furniture that costs $1,520. The store will allow you to make weekly payments of $32.33 for one year to pay off the loan. What is the EAR of this arrangment?

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Franco Cooke · Answer 1

The EAR of this arrangement is 22.24%.

Explanation:

The choice given by the store means that the present value of 52 weekly equal payment discounting at a weekly discount rate will be equal to the furniture price which is $1,520 (as one year has 52 weeks). So, we apply the formula for calculating the present value of the annuity, with x denoted as discount rate as below:

1,520 = (32.33/x) * [1 - (1+x) ^ (-52) ] x = 0.387%.

As x = 0.387% is weekly rate, the EAR will be calculated as:

EAR = [ (1+0.387%) ^ (52) ] - 1 = 22.24%.