# 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: 571. This question is similar to one that appeared on an IB AA Standard paper in 2021. The use of a calculator is allowed.

Two friends Arthur and Babette, each set themselves a target of saving £12000. They each have £6800 to invest.

(a) Arthur invests his £6800 in an account that offers an interest rate of 8% per annum compounded annually. Find the value of Arthur's investment after 6 years.

(b) Determine the number of complete years required for Arthur's investment to reach the target.

Babette invests her £6800 in an account that offers an interest rate of $$r$$% per annum compounded monthly, where $$r$$ is set to two decimal places.

(c) Find the minimum value of $$r$$ needed for Babette to reach the target after 15 years.

A third friend Callum wants to reach a £9000 target. He puts £4000 under his mattress where it does not earn any interest. His system is to add more money to his savings regularly. Each year he will add half the amount added in the previous year.

(d) Show that Callum will never reach the target if during the first year he adds £2000.

(e) Find the amount Callum needs to add during the first year in order to reach the target after 8 years.

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