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Debt Race

Age 16 to 18
Challenge Level Yellow star
  • Problem
  • Getting Started
  • Student Solutions

On 1st June 2008 five people A, B, C, D and E each borrow $100,000.

Each year, starting 1st June 2009, each is charged interest on the amount owed at the start of the previous year, which is added to the balance. Each year, each will pay off a lump sum of their debt, which is taken from the balance.

The rates and amounts for each borrower is as follows:

A B C D E
3% 6% 9% 12% 15%
$12,000 $14,000 $16,000 $18,000
$20,000

The question is this: Which borrower will be the first to pay off their debt?

Extension: You might like to consider the importance of the figure $100,000 in this calculation

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The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.

NRICH is part of the family of activities in the Millennium Mathematics Project.

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