TOPIC 2 FINANCIAL MATHEMATICS

Question 1.1

Your parents put some money in the bank 20 years ago for you to go to university. The interest rate was 5% p.a. compounded quarterly. Today, they have you the amount of that investment which is $115 352. How much did your parents originally put in the bank? Show all workings.

Question 1.2

a) How much will you have in the bank if you invest $40 000 today at an interest rate of 7% p.a. compounded fortnightly in 8 years from today?

b) What is the effective annual interest rate on your investment?

Question 1.3

An investment that a friend has recommended has the following cash flows:

End of Year 1$25 000

End of Year 2$16 000

End of Year 3$28 000

End of Year 4$32 000

End of Year 5$40 000

How much is the investment worth today, if the required rate of return is 5% p.a.?

Question 1.4

a) Calculate your monthly loan repayments on a 30-year $650 000 mortgage, at an interest rate of 4% p.a.

b) Would the amount change if repayments are made at the start of the month? If so, calculate this amount.

Question 1.5

a) How much do you need to invest per quarter in order to have $2 000 000 in 20 years time at an interest rate of 8% p.a.?

b) Would the amount change if contributions are made at the start of the quarter? If so, calculate this amount.

Question 1.6

a) What is the price today of an investment that promises to pay $400 per month for 10 years at an interest rate of 9% p.a.?

b) Would the amount change if returns are received at the start of the month? If so, calculate this amount.

Question 1.7

a) How much will you have in an investment that you invest $15 000 semi-annually in for 30 years at a return of 6% p.a.?

b) Would the amount change if contributions are made at the start of each 6 month period? If so, calculate this amount.

Question 1.8

How much would you be prepared to pay today for an investment that will pay you $25 000 annually at a return of 5% p.a. forever?