Ethan is planning to join a health club. He can pay $225 for one year's membership, or he can pay $30 per month for 12 months. What percent discount does he receive for paying in full?
The best way to take care of this question is to look at how much each approach costs, and consider how much he saves by buying the whole year rather than by going month-to-month.
Paying for the whole year is given in the question: $225
Paying for the whole month requires us to multiply the monthly rate by 12 for each month in the year:
Cost for approach 2: `$30xx 12 = $360`
To calculate the discount, we consider the difference over the original cost:
`D = ($360-$225)/($360) = ($135)/($360) = 0.375`
To get the desired percentage, we simply multiply by 100 and denote with a percentage symbol, giving us the discount he receives: 37.5%.
When Ethan joins the cub he has the option of paying his membership as a single amount of $225 for the whole year or as 12 monthly amounts of $30.
If he opts for the monthly payment option he pays 12*30 = $360
This is $360 - 225 = 135 greater than the annual fee. The discount he gets if he opts of the annual membership option is `(135/225)*100 = 37.5%`