Question

You are considering buying the latest stereo system model. The dealer in "The Stereo World" store has offered you two payment options. You can either pay $10,000 now, or you can take advantage of their special deal and "buy now and pay a year from today," in which case you will pay $11,100 in 1 year. Calculate the effective annual interest rate (EAIR) of the store's special deal.

Answer 1

The effective annual interest rate (EAIR) for the store's special deal is calculated by comparing the future payment to the present value, which results in an EAIR of 11%.

Step-by-step explanation:

To calculate the effective annual interest rate (EAIR) of the store's special deal, we need to compare the amount of money that would be paid now versus the amount that would be paid in the future. According to the offer, you can pay $10,000 now or $11,100 in one year. The difference in payments is due to the interest that would be accrued over the year.

Step-by-Step Calculation

1. Take the future payment amount and divide it by the present payment amount: $11,100 / $10,000 = 1.11.
2. Subtract 1 from this result to find the interest rate: 1.11 - 1 = 0.11.
3. Express 0.11 as a percentage to find the EAIR, which is 11%

Thus, the effective annual interest rate for choosing to pay later rather than paying upfront is 11%.