Question 2 (15 marks, 5 marks for each part)

a. Roger has invented a new household device that would earn him $10,000 per annum for the next 10 years. Given an interest rate of 8% per year, would Roger be willing to sell his invention today for $100,000?

b. Debra wins $200,000 in a lottery. She takes only $20,000 in cash and invests the balance at a rate of interest of 10% pa with the understanding that she will receive 160 equal monthly payments with the first one to be made in 2 years. Find the size of the payments.

c. An investment firm A pays 10% interest per annum, compounded on a quarterly basis. To remain competitive, the investment manager of another firm (firm B) is willing to match the interest rate offered by firm A, but interest will be compounded on a monthly basis. What nominal rate of interest must firm B offer to its clients?
Question 3 (15 marks, 5 marks for each part)

You have had your offer of $1,000,000 on a house accepted and have arranged with the bank for a 25 year mortgage equal to 90% of the sale price. The agreement calls for monthly repayments and the bank will charge a nominal annual interest rate of 6%.

a. If the first payment is due one month after the loan is received, calculate the amount for the regular installments.

b. After the 36th payment the interest rate decreases to 5% p.a. Assume you have decided to maintain the monthly repayment. If you choose to pay out the mortgage after the 36th payment, what is the payout figure?

c. If you choose not to pay out the mortgage after the 36th payment, how much longer will it take you to pay out the loan?

Question 4 (15 marks, 5 marks for each part)

The following table provides the share return forecasts and associated probabilities for ASR Limited and RDL Limited. Answer parts a. to c. using the information provided. Detailed worked solutions must be presented in your answers, including formulae used, progressive and final answers to the questions.

ASR Limited RDL Limited
Return Probability Return Probability
18.50% 50.00% 16.50% 50.00%
14.00% 20.00% 10.50% 20.00%
9.50% 30.00% 7.00% 30.00%

a. Calculate the expected return on each share.
b. Calculate the variance and standard deviation for each share.

c. Suppose a portfolio comprised of 40% investment in ASR Limited and 60% investment in RDL Limited can be constructed. An analyst has estimated that the correlation coefficient of the two-asset portfolio is -0.40, calculate the return and standard deviation of this portfolio. Compare your answer with those reported in parts a. and b. and draw your conclusion.

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