a. An investment scheme pays $200 at the end of each of the next 4 years, $400 at the end of year 5, $300 at the end of year 6 and $500 at the end of year 7. Given that other investments of equal risk earn 10% per annum, calculate the present value and future value of this investment.
b. George won a lottery of $200,000. He invested the entire amount and expects a yearly return of 10% per annum on his investment and he will receive 150 equal monthly payments. The first payment is expected in 2 years. Find the size of the payments.
c. Excel Bank pays its clients 10% interest per annum, compounded on a quarterly basis. To remain competitive, the bank's major competitor, Advanced Bank is willing to match the interest rate offered by Excel Bank, but interest will be compounded on a monthly basis. What nominal rate of interest must Advanced Bank offer to its clients?
Question
You have had your offer of $600,000 on a house accepted and have arranged with the bank for a 30 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 7%.
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 increases to 10% 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
The following table provides the share return forecasts and associated probabilities for Advanced Limited and Bright 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.
| Advanced Limited |
|
Bright Limited |
|
|
|
|
|
| Return (%) |
Probability (%) |
|
Return (%) |
Probability (%) |
| 15.5 |
30 |
|
20.3 |
20 |
| 12.0 |
30 |
|
10.5 |
50 |
| 9.5 |
40 |
|
7.0 |
30 |
|
|
|
|
a. Calculate the expected return on each share.
b. Calculate the variance and standard deviation for each share.
c. Suppose a portfolio comprised of 60% investment in Advanced Limited and 40% investment in Bright Limited can be constructed. An analyst has estimated that the correlation coefficient of the two-asset portfolio is -0.50, calculate the return and standard deviation of this portfolio. Compare your answer with those reported in parts a. and b. and draw your conclusion.