An electronics store offers you no interest financing for one year on a $1000 flat-screen television. A nearby electronics store offers the same television on sale at $985. You have set aside $1000 for this purchase in your bank account that earns 3% interest annually. Which offer is a better deal?
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To determine which offer is a better deal, you need to compare the amount of money you would spend or save in each scenario after one year.
Scenario 1: No interest financing for one year at $1000. In this scenario, you do not pay any interest on the purchase of the television, and you can keep your $1000 in the bank to earn interest for a year. The interest you would earn on $1000 at a 3% annual rate is:
Interest = Principal × Rate × Time Interest = $1000 × 0.03 × 1 Interest = $30
At the end of one year, you would have earned $30 in interest, making your total balance $1030.
Scenario 2: Buying the television outright for $985. If you choose to purchase the television for $985, you would spend less upfront compared to the $1000 offer, and you would have $15 left to keep in your bank account. This $15 would also earn interest for a year at 3%, which would be:
Interest = Principal × Rate × Time Interest = $15 × 0.03 × 1 Interest = $0.45
Therefore, at the end of the year, you would have:
Television cost: $985 Remaining balance + interest: $15 + $0.45 = $15.45 Total cost after interest earned: $985 + $15.45 = $1000.45
Since in Scenario 1, you end up with $1030 after earning interest on the full $1000, and in Scenario 2, you spend $985 and have $15.45 left after interest, the better deal comes down to comparing $1030 - $1000 (the cost of the TV on financing) versus the outright cost of the $985 TV.
The difference in Scenario 1 is: $1030 (what you end up with) - $1000 (the cost of the TV) = $30 (the gain for keeping your money in the bank)
Therefore, the first offer of no interest financing for one year at $1000 is a better deal because you effectively pay less for the television after accounting for the interest you'd earn on your $1000 if left in the bank.