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The Real Cost of Your First Car

Algebra

'Only Β£199 a month!' β€” but what does the car actually cost you? Take apart a real finance offer: deposit, monthly payments, the balloon at the end, and the value the car quietly loses the whole time.

Where this idea comes from

Start here β€” these are the sources that inspired this exploration.

Introduction

Most first cars aren't bought β€” they're financed. A typical offer has a deposit, a couple of years of monthly payments, and a large optional 'balloon' payment at the end if you want to keep the car. Meanwhile the car itself is losing value every month. Both sides of this are mathematics you can do: the payments are a loan you can take apart with your calculator's finance tools, and the falling value is a curve you can fit from real second-hand listings β€” the same shape you'll find in our Car Showroom dataset. The question that matters: by the end of the deal, what did you pay, and what do you own?

Guiding Questions
  • Find a real finance offer for a car you'd actually want: deposit, monthly payment, length, balloon payment, and the cash price. Total everything β€” how much more than the cash price is the finance route?
  • Use your calculator's finance solver to find the interest rate buried in the offer. How does it compare with the rate printed in the small print?
  • Now the other side: collect asking prices for the same model at different ages and fit a curve. How much value does the car lose during your finance term?
  • Put the two together: at the end of the deal, compare what you've paid with what the car is worth. Was the balloon payment set fairly?
  • Change something about the deal β€” your choice β€” and find out what the seller least wants you to change.
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Key Mathematical Concepts
Modelling Financial Mathematics Interest Rates Amortisation Depreciation
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