# Exam-Style Question on Finance

## A mathematics exam-style question with a worked solution that can be revealed gradually

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Question id: 444. This question is similar to one that appeared on an IB AI Standard paper (specimen) for 2021. The use of a calculator is allowed.

Mr and Mrs Moule are considering purchasing a new car with a price of £12000

The dealership offers two options to finance a loan.

### Finance Plan A:

A five year loan at a nominal annual interest rate of 12 % compounded quarterly. No deposit is required and repayments are made each quarter.

(a) Find the repayment made each quarter.

(b) Find the total amount that will have been paid for the car by the end of the five years.

(c) Find the total amount interest that will have been paid on the loan by the end of the five years.

### Finance Plan B:

A five year loan at a nominal annual interest rate of $$r$$% compounded monthly. An Initial 12% deposit is required and monthly repayments of £255.

(d) Find the annual interest rate, $$r$$.

(e) State which option Mr and Mrs Moule should choose and justify your answer.

This new car will depreciates at an annual rate of 20% per year.

(f) Find the value of Mr and Mrs Moule’s car when it is ten years old.

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