Miguel just graduated from university. He plans to work for 5 years and then study a PhD degree. He figures he can save $5000 in the first year and will be able to save 10% more than the previous year in each of the next 4 years. His saving account pays an interest rate of 6.6% p.a. and the interests are compounded annually.

a) How much will Miguels saving account be able to accumulate 5 years later? [4 marks]

b) If Miguel also puts his parents graduation gift of $3000 into his saving account at the beginning of the 5 years, what will be his total saving account balance 5 years later? [4 marks]

c) Miguel plans to withdraw an equal monthly amount during the 4 years of his PhD study (starting one month after he commences his PhD) so that he will just exhaust his savings, i.e. the answer to part b) at the end of his 4-year study. If his saving account still pays an interest rate of 6.6% p.a. during these 4 years, but compounded monthly, how much can he withdraw per month? [3 marks]

d) Assume Miguel still has to take a student loan to support his living expense during his PhD study. If the loan pays him $400 per month for 4 years (starting one month after he commences his PhD) with an interest rate of 3.6% p.a. compounded monthly, what is his outstanding loan account balance 4 years later right after his completion of the PhD degree? [3 marks]

e) According to the agreement, Miguel has to pay back the loan balance in 15 years with the same repayment amounts. If the bank offers Miguel two options to repay the loan, calculate and identify which option Miguel should accept? [6 marks]

Option 1: Annual percentage rate of 3.4% and the repayments are made per fortnight.

Option 2: Annual percentage rate of 3.6% and the repayments are made monthly