Exam-Style Question on Finance
A mathematics exam-style question with a worked solution that can be revealed gradually
Question id: 15. This question is similar to one that appeared on an IB Studies paper in 2010. The use of a calculator is allowed.
All answers to this question should be given to the nearest whole currency unit.
Katie and Keith each have 9000 USD to invest.
Katie invests her 9000 USD in a bank account that pays a nominal annual interest rate of 3.8% compounded yearly. Keith invests his 9000 USD in an account that offers a fixed interest of 410 USD each year.
(a) Find the amount of money that Keith will have in the bank after 4 years.
(b) Find the amount of money that Katie will have in the bank at the end of 9 years.
(c) Find the number of complete years it will take for Katie’s investment to first exceed 12000 USD.
(d) Find the number of complete years it will take for Katie’s investment to exceed Keith’s investment.
Keith moves from the USA to Spain. He transfers 3500 USD into a Spanish bank which has an exchange rate of 1 USD = 0.89 euros. The bank charges 1.5% commission.
(e) Calculate the amount of money Keith will invest in the Spanish bank after commission.
Keith returns to the USA for a short holiday. He converts 900 euros at a bank in Rutherford, NJ and receives 1018.44 USD. The bank advertises an exchange rate of 1 euro = 1.15 USD.
(f) Calculate the percentage commission Keith is charged by the bank.
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