QUESTION 1
Mary purchased a 180-day $100 000 bank bill at a yield of 5% p.a. (simple interest) on 15 April 2016. She sold the bank bill on 6 June 2016 at yield of 4.5% p.a. (simple interest).
a. Draw a carefully labelled cash flow diagram (from Mary's perspective) to represent the above financial transactions.
b. What was her selling price?
QUESTION 2
A donor gives $500 000 to establish a fund to provide an annual prize in perpetuity. Assume the fund will earn ji = 3% p.a. and the prize will be first awarded 2 years after the date of the donation.
a. What is the amount of the annual prize?
Ten years later; just after giving the annual prize, the fund is affected by a global financial crisis and its size is reduced by 20%. If the fund is to continue offering annual prizes in perpetuity (at a rate of 3% p.a. effective) the amount of the annual prizes must be adjusted.
b. Draw a carefully labelled cash flow diagram to represent the above circumstance. Draw your diagram from the perspective of the prize fund.
c. What is the new amount of the annual prize?
QUESTION 3
In 2015 Sun purchased a Treasury bond, redeemable at par (i.e., for $100) on 15 November 2025. The coupon rate is 5.5% p.a. payable half-yearly. Sun purchased the bond at a yield of 6% p.a. compounded half-yearly.
a. If Sun purchased this bond on 22 March 2015, draw a care-fully labelled cash flow diagram to model the above financial transac-tion. Draw your cash flow diagram from Sun's perspective.
b. What did Sun pay on 22 March 2015 for the bond?
c. If Sun had waited till 10 May 2015 to purchase this bond, what would he have paid?
QUESTION 4
At the beginning of 2016 John was planning to set up an education fund for his 4-year-old son Charlie's future HECs fees. Assume that Charlie will go to university in 2030 (14 years later). His HECs fees will be paid at the start of year in 2030, 2031 and 2032 with the predicted amounts being $21500, $23000 and $25000, respectively. Use an interest rate of j4 = 7% p.a. in your calculations.
a. At the beginning of 2030, immediately before Charlie's first HECs payment, what is the present value of Charlie's HECs fees?
At the beginning of 2016 John set up the fund and made a deposit of $3 000 into it. He is planning to make 14 equal annual deposits-the first will be made at the start of 2017-so that the fund can pay Charlie's HECs fees as they fall due.
b. Draw a carefully labelled cash flow diagram that models the above situation. Draw your cash flow diagram from the perspective of the education fund.
c. Determine what John must contribute to the fund over the fourteen years such that it accumulates to an amount sufficient to meet Charlie's HECs fee payments.
QUESTION 5
Jessica has borrowed $1000000 from First Bank for one year. Her under-standing of the terms of the loan is that she will be charged 3% p.a. simple interest in one years' time.
a. What is the total amount (principal and interest) Jessica thinks she needs to repay in one years' time?
Jessica thought the interest rate being charged was 3% p.a. simple interest. It turns out she made a mistake and was, in fact, told by the bank that her interest rate was 3% p.a. compounded half-yearly (i.e., j2 = 3% p.a.).
b. What is the extra amount that Jessica needs for the total repayment at the end of the year?
After some negotiation, First Bank allows Jessica to use 3 equal monthly instalments, paid by at the end of each month, at 5% p.a. compounded half-yearly, to repay the extra amount discussed in b. The first payment will occur one month after the one year term of the loan expires.
c. Draw a carefully labelled cash flow diagram (from Jessica's perspective) to represent the above financial transactions.
d. What is the instalment amount?