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?

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%.

deebikamadhivanan deebikamadhivanan · Answer 2 · 2022-03-02T04:25:48+01:00

The real interest rate for a year is the effective yearly rate. is the nominal interest rate, sometimes known as the "stated rate," expressed in percent. This arrangement's EAR is 22.24%.

What is the EAR computation?

The store's selection means that the present value of 52 weekly equal payments discounted at a weekly discount rate equals the $1,520 furniture price ( as one year has 52 weeks).

As a result, we use the following formula to calculate the present value of the annuity, with x designated as the discount rate:

[tex]1,520 = (\frac{32.33}{x} ) \text{ x } [1 - (1+x)^{-52} ]\\\\x = 0.387%.\\\\\\\\As x = 0.387 \text{ is weekly rate the EAR will be calculated as:}\\\\EAR = [ (1+0.387)^{52} ] - 1 \\\\EAR = 22.24%.[/tex]

Note: 0.387 is 0.387%

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