Pleasehelpmeanswerthesequestions:

Mrs Okoth invests a sum of money for her retirement which is expected to be in 20 years' time. The

money is invested in a zero coupon bond which provides a return of 8% per annum effective. At

retirement, she requires sufficient money to purchase an annuity certain of KES 1,200,000 per annum

for 25 years. The annuity will be paid monthly in arrear and the purchase price will be calculated at a

rate of interest of 6% per annum convertible half-yearly.

(i.) Calculate the sum of money she needs to invest at the beginning of the 20-year period. [7]

Over the 20-year period the Consumer Price Index has changed in value from 103 at the beginning of

the 20-year period to 353 at the end of the 20-year period

(ii.) Calculate the annual effective real return Mrs Okoth would obtain from the zero coupon bond [4]

2. Your daughter has just joined form three and is keen to join university immediately after completing high school to pursue her dream of studying interior design. As a forward looking parent you would like to invest part of your just received bonus payment as a lump sum in order to have university fees readily available when the time comes. You estimate that you will require KES 250,000 per year at the beginning of each university year (ignoring inflation) for the 5-year degree programme.

(i.) How must should you invest as a lump sum now if you can earn a rate of interest 8% annually on investments? [4]

(ii.) Suppose you opt to open a bank account that pays interest 5% per annum and deposit a level sum into it monthly for the next 7 years (2 years whilst she is still in high school and 5 years during her university education). How much would you need to deposit each month in order to have a nil balance in the account at the end of your daughter's education?

[You will also withdraw from this account annually to pay university fees.] [10]

3. An investor wishes to purchase a 10-year level annuity due that is payable half-yearly. The first payment will be made in 2 years. Calculate the amount of each payment if the purchase price is $10,000 and the effective interest rate is 8% pa.

4. Thanos, a powerful supervillain, believes that he will live forever and would like to purchase a perpetuity to provide him with a regular quarterly income as he causes chaos in the Marvel galaxy. Determine the amount of quarterly income he will receive if he pays a purchase price of $250Mn. Effective interest is 10% per annum. [3]

Question 7 An Economy of a country produces these 2 goods in 2012, 2013, 2014 Quantity Price Quantity Price Quantity Price 2012 2012 2013 2013 2014 |2014 Textile 100 1 90 1.5 120 2 Electronics 200 7 200 8 210 8 A) Assuming that 2012 is the base year, complete the following table (show your calculation) Nominal Real Deflator GDP GDP 2012 2013 2014 B) Calculate the growth rate and inflation rateB) Calculate the growth rate and inflation rate Growth rate Inflation rate 2012/2013 2012/2014 C)-Determine the Real GDP in 2015 if economists forecast 3.5 % recession. D).Draw the GDP fluctuation graph, starting 2011 till 2015 and label each phase.13. Your have decided to invest all your wealth in two mutual funds: A and B. Their returns are characterized as follows: . the mean returns are FA = 20% and Fe = 15% . the covariance matrix is TA IB TA 0.3600 0.0840 TB 0.0840 0.1225 21 5 2005, Andrew W. Lo and Jiang Wang 1.6 Risk & Portfolio Choice 1 QUESTIONS You want your total portfolio to yield a return of 18%. What proportion of your wealth should you invest in fund A and B? What is the standard deviation of the return on your portfolio? 14. In addition to the fund A and B in the previous question, now you decide to include fund C to your portfolio. Its expected return is fc = 10%. The covariance matrix of the three funds is TA TB rc TA 0.3600 0.0840 0.1050 TB 0.0840 0.1225 0.0700 rc 0.1050 0.0700 0.0625 Your portfolio now consists of fund A, B and C. You would like to have an expected return of 16% on your portfolio and a minimum risk (measured by standard deviation of the return). What portfolio should you hold? What is the return standard deviation of your portfolio? (Hint: You would need to use Excel Solver or some other optimization software to solve the optimal portfolio.) 15. You can only invest in two securities: ABC and XYZ. The correlation between the returns of ABC and XYZ is 0.2. Expected returns and standard deviations are as follows: Security | E[R] o(R) ABC 20% 20% XYZ 15% 25% a) It seems that ABC dominates XYZ in that it has a higher expected return and lower standard deviation. Would anyone ever invest in XYZ? Why? b) What is the expected return and standard deviation of a portfo- lio that invests 60% in ABC and 40% in XYZ? c) Suppose instead that you want your portfolio to have an expected return of 19.5%. What portfolio weights do you select now? What is the standard deviation of this portfolio