Today is 1 July 2019. John is 30 years old today. He is planning to purchase an apartment with the price of $800,000 on 1 January 2024. John believes that, at the time of purchasing the house, he should have savings to cover 20% of the house price (i.e., $160,000) on 1 January 2024. John has a portfolio which consists of two Treasury bonds and a bank bill (henceforth referred to as bond A, bond B and bank bill C). There are 200 units of bond A, 300 units of bond B and 400 units of bank bill C.

a)

Bond A is a Treasury bond which matures on 1 July 2030. One unit of bond A has a coupon rate of j2 = 3.95% p.a. and a face value of $100. John purchased this Treasury bond on 15 February 2017. The purchase yield rate was j2 = 3.85% p.a.

Bond B is a Treasury bond which matures on 1 January 2026. One unit of bond B has a coupon rate of j2 = 3.7% p.a. and a face value of $100. John purchased this Treasury bond on 1 July 2016. The purchase yield rate was j2 = 4.1% p.a.

Bank bill C is a 180-day bank bill which matures on 1 September 2019. One unit of bank bill C has a face value of $100. John purchased this bank bill on 15 April 2019. The purchase yield rate was 3.05% p.a. (simple interest rate).

Calculate:

The purchase price of one unit of bond A

The purchase price of one unit of bond B

The purchase price of one unit of bank bill C

b. John decides to sell each of the three security types today. Both the bonds are sold at a yield rate of j2 = 3.2% p.a. and the bank bill is sold at 3% p.a. (simple interest rate).

Calculate The sale price of one unit of bond A

The sale price of one unit of bond B

The sale price of one unit of bank bill C

Round your answer to three decimal places. Then calculate the total sale price of the portfolio (round your answer to the nearest dollar). Note that the sale of each bond occurs after a coupon payment.

c. John plans to use $80,000 of the sale proceeds calculated in part b to invest into a fund today. John predicts that the return rate of this fund will be 1 July 2019 to 30 June 2021 j2 = 5.1%, 1 July 2021 to 31 December 2023 j2 = 5.3%. Calculate the accumulated value of Johns fund investment on 1 January 2024.

d. To save for remaining required amount on 1 January 2024 (the difference between the 20% of the house price and the accumulated value from part c), John plans to deposit z% of his annual after-tax salary into a saving account on 1 July of each year from 2019 to 2023 (5 deposits in total). The saving account rates are assumed to be 0.2% per month. Assume that Johns after-tax salary is $90,000 p.a. Find the value of z (expressed as a percentage and rounded to two decimal places).

e. From Johns perspective, draw a carefully labelled cash flow diagram to represent the above financial transactions of parts c and d.