Topic 3 Tutorial Questions PDF

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FINC5001

Topic 3 – Financial Mathematics II Tutorial Questions

Question 1 Suppose you deposit $500 in an account at the end of each month at 12% pa compounded monthly. How much will you have in 5 years’ time?

Question 2 My HSBC Serious Saver Account is offering 0.70% p.a. compounding daily for every month that I do not make a withdrawal. Suppose I deposit $875 at the end of every month into this account. How much will I have by the end of 3 years?

https://www.hsbc.com.au/accounts/products/serious-saver/

Question 3 Uncle Fred has asked for your help regarding his plans for retirement. He thinks he will need $100,000 p.a. for living expenses from his 67 st birthday to his 90 th birthday inclusive. You estimate that he can earn 7% p.a. compounding annually over that time. a) How much will he need in his retirement savings account when he retires on his 66 th birthday to provide for these payments? b) Upon reflection, Uncle Fred realises that he would need the annual payments to increase over time in line with the expected inflation rate of 2.5% p.a. If the payment on his 67 th birthday is $100,000, how much will he need on his 66th birthday to provide for these payments?

Question 4

https://www.stgeorge.com.au/personal/home-loans/our-home-loans/fixed-rate-home-loan

Harry and Meghan take out a 20-year housing loan for $500,000 with monthly repayments from St George Bank. They agree to a fixed rate of 2.89% p.a. compounding monthly for 3 years. After the first 3 years, it is converted into a variable rate loan. a) Calculate the repayment for the first 3 years. b) If Harry and Meghan make their repayments as scheduled for the first 3 years of the loan, calculate the amount of the loan still outstanding after 3 years. c)

They then switch to a variable rate loan where the interest rate is initially 3.6% p.a. compounding monthly. Calculate the monthly repayment now required.

Question 5 Congratulations on expecting your first child! Your parents would like to invest a sum of money on the day the baby is born to provide for 5 annual payments of $50,000 to cover the expenses of the child’s university education. The first payment is to be made on the child’s 19th birthday, and interest is 5% p.a. compounding annually. How much will your parents need to invest?

Question 6 Starbucks is considering the purchase of new a machine for producing flavoured syrups from a choice of two. Both perform the same function. Machine 1 has a useful life of 5 years whilst Machine 2 lasts for 8 years, and there is the expectation they will be replaced at the end of their lives with an identical machine for an indefinite period. The initial and annual costs of running each machine are given below ($ millions). Year Machine 1

0 -20

1 -5

2 -5

3 -5

4 -5

5 -5

6

7

8

Machine 2

-10

-7

-7

-7

-7

-9

-9

-9

-9

a) Calculate the (net) present value of these two machines at a cost of capital of 10% p.a. compounded annually. Which machine has the lower cost? b) Since the projects are of different lengths, their present values are not directly comparable. Now use the present values that you calculated in part (a) to find an equivalent annual payment (PMT) for each machine. Which machine would you now recommend that Starbucks purchase?

Question 7 You have just taken delivery of your new Tesla Model S and wish to arrange comprehensive insurance for your new car. NRMA have quoted you a monthly premium of $574.88, payable in advance. What annual premium (also payable in advance), would be equivalent at an interest rate of 5.4% p.a. compounding annually?

Question 8 Your company is deciding between two investment choices: one that pays $100 per year in perpetuity, and another that pays $100 per year for 100 years. The current market interest rate for investments of similar risk is at 10% p.a. What is the present value of these two investments? Why are they so similar?...