Question 1:

Jessica opened a bank account with an initial deposit of $10,000. The bank account pays monthly interests at 6% p.a. convertible monthly.

(a) How much will Jessica accumulate in 5 years if she is not going to make further deposits?

(b) Jessica plans to withdraw $5000 from this account in 6 years' time and the remaining balance $X in 8 years' time. Calculate the value of X.

Question 2:

A loan is borrowed to make a purchase. The loan is going to be repaid by 3 instalments. The first instalment will be $1,000 in 4 months, the second instalment will be $1,200 in 8 months and the final instalment will be $1,500 in 12 months.

(a) Calculate the value of the loan if the bank charges interest at 12% p.a. compounded monthly.

(b) Calculate the value of the loan if the bank charges interest at 12% p.a. compounded quarterly.

Question 3:

Investor A contributes 40 payments of $2,000 at the end of each year into a funduntil his 60th birthday. The fund earns 8% effective annual return.

(a) How much will be in the fund immediately after the final deposit?

(b) Assume no further contribution is made, how much will be in the fund on the investor's 65th birthday?

Question 4:

Mike deposits a single payment into a fund on 1 July 2013. Mike will make quarterly withdrawals of $1,000 for 5 years (i.e. 20 withdrawals will be made). Interest is at 10% p.a. convertible quarterly. Calculate the size of the initial deposit if

(a) the first withdrawal is on 1 October 2013 (one quarter after 1 July 2013);

(b) the first withdrawal is on 1 July 2014 (four quarters after 1 July 2013).

Question 5:

A company wishes to accumulate $50,000 by the end of 5 years. What level deposit should be made at the end of each quarter for 5 years if interest is at 12% p.a. compounded monthly?

Question 6:

(a) How much money $X is required to establish a scholarship paying $10,000 per year in perpetuity, if interest is at7% p.a. effective?

(b) Jack has to make a choice between two bank saving accounts. CBA offers 6% p.a compounded monthly whereas ANZ offers 6.4% compounded semi-annually. Assume Jack prefers higher return, provide a suggestion and justify with calculation.

Question 7:

A bond with face value of $1000 and semi-annual coupon rate 8% is to be redeemed at par in 6 years. Assume market yield is 10% p.a. compounded semi-annually.

(a) Determine the current market price of the bond.

(b) Answer the following question without calculation.Assume the market interest rate decreases to 6%, will the bond price be higher or lower than $1000? Briefly justify your conclusion.

Question 8:

(a) TLSA Ltd paid 50 cents dividend yesterday and expect that to grow at 4% p.a. infinitely. If the required rate of return is 15%, calculate the current share price of TLSA.

(b) Norm Ltd is expected to pay $1 annual dividend per share in the next three years but reduce that to $0.5 per share infinitely. Calculate the share price of Norm Ltd assuming 12% required rate of return.

(c) HVA Ltd is expected to make the first dividend payment of $0.8 per share in 4 years. The dividend will grow by 3% each year infinitely. Calculate the current share price of HVA assuming 16% required rate of return.

Question 9:

What is a principal-agent problem that may exist in a company? Give one example of this problem in reality. Briefly explain how is this problem addressed in practice? (limit your answer to 200 words)