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.

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

The price of both bond A and B should be calculated by using the RBA method.