Math Journal: Converting percents to dollars for Housing Development Fund

On Wednesday (July 31, 2019) Bloomington’s city council will consider the first reading of a rezoning request from the Collegiate Development Group to build an 820-bedroom student housing project on North Walnut Street at the site of the current Motel 6.

CDG location map iso Screen Shot 2019-07-29 at 11.01.38 AMOne point likely to be raised is the amount of money CDG has committed to pay into the city’s Housing Development Fund, in connection with the proposed project. It’s a fund that was created by unanimous city council vote on Nov. 16, 2016.

The amount of CDG’s commitment to the Housing Development Fund is not expressed as a fixed dollar amount. The amount depends on a percentage of the number of bedrooms that are built.

Doesn’t CDG know already how bedrooms are in the project? It’s probably fair to say that CDG knows how many bedrooms it would like to build into the project, namely 820. But based on some early reaction from some councilmembers, at their July 19 work session, they might want to see the number of bedrooms reduced in order to approve the re-zoning.

Given the way that CDG has expressed its commitment, a reduction in the number of bedrooms will cause a reduction in the amount that CDG will pay into the Housing Development Fund.

Here’s what CDG says in its letter:

…CDG will commit a contribution (“Contribution”) in the amount of $20,000.00 per bed for 15% of the total beds on the property located at 1800 N. Walnut Street to the City of Bloomington Housing Development Fund. CDG will memorialize this contribution as part of a zoning commitment that will be filed with the Monroe County Recorder’s Office. CDG will pay 25% of the total contribution upon receipt of building permits for the Project. The remainder of the commitment will be paid upon receipt of an occupancy permit for the property.

So it’s important to be able to calculate the amount of the contribution if the number of bedrooms changes. That’s the idea behind the problem presented below.

Feel free leave your answer to the problem as a comment. If The Beacon has set up the commenting system correctly, your correct answer won’t spoil things for other people, because it will sit unseen, until it gets “approved.” After a month or so, any comments with correct answers will be approved. (If this website manages to turn a profit, maybe correct answers to future real-world math problems from The Beacon’s Math Journal will be rewarded with some kind of prize. But it’s not there, yet.)

Housing Development Fund Percent Problem

If CDG’s proposal for 1800 N. Walnut is approved with 820 bedrooms (one bed per bedroom), how much money will CDG pay as a contribution to Bloomington’s Housing Development Fund when CDG receives its building permits? (Show your work!)