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Your brother Gavin and his wife Lisa have a newborn son, Martin. They are saving for their son's university education.

Your brother Gavin and his wife Lisa have a newborn son, Martin. They are saving for their son's university education. They estimate that university expenses will run at $40 000 per year when their son reaches university in 18 years. The annual interest rate over the next few decades will be 4 per cent per annum. Your grandfather is also very happy. He has $10 000 now and wants to put it into a bank saving account for 5 years, and will use the accumulated money to then buy a decent present for his grandson, Martin. He is considering four banks. The Commonwealth (Bank) is within walking distance, pays 5% annual interest compounded quarterly, and provides free coffee in the morning. The NAB is in town, and pays 5% interest compounded daily. Getting to this bank requires a train trip, but your grandfather can use his senior card for free rides. However, more importantly, this bank does not serve free coffee. The ANZ is next door to the NAB, and also serves free coffee. But this bank pays 5% annual interest compounded continuously. Westpac is next door to the Commonwealth and pays 5% annual interest compounded yearly. This bank also serves free coffee. (a) How much money must your brother Gavin and his wife deposit in the bank each year so that their son will be completely supported through four years of university? Show all the necessary working steps. (Note: to simplify the calculations, we assume that Martin is born today — date 0. His parents will make the first of his four annual tuition payments on his 18th birthday. They will make equal bank deposits on each of his first 17 birthdays, but no deposit at date 0.) (5 marks) (b) Which bank should your grandfather select? Show all the necessary working steps and explain why?

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