Paul is a social worker. He lives with his wife in a village in New Territories. He has an outstanding fixed mortgage payment of $15,000 per month for 5 years. The interest rate is fixed at 5% p.a. He wishes to advance his mortgage payment by two years by paying a lump sum (i.e. pay at Year 3). Paul and his wife, Pauline have a 10-year old daughter, Polly. They wish to send her daughter to a UK university for 4-year study in 8 years time. It is expected to cost $250,000 for every 6-month in present value terms. Paul intends to make an initial contribution of $800,000. After that, he believes he can make $3,000 regular contribution for every 6-month (starting at t = 0.5) while he is paying the mortgage. This contribution is expected to grow with an inflation rate of 3%. After repayment his mortgage in 3 years time, he believes he can make an extra contribution of $7,500 per month (or $45,000 for every 6-month (starting at t = 3.5). Again, this contribution is expected to grow with inflation rate.

a. Assume there are no extra interest and handling charges, what will be the amount he needs to repay the bank if he wants to repay all his mortgage by 2 years? (6 marks) Hints: = 1 () where c, r and t are periodic payment, periodic interest rate and number of periods respectively.

b. Estimate Pauls daughter education expenses at t = 8, 8.5, , and 11.5. (4 marks)

c. Estimate Pauls regular contributions while he is still payment the mortgage at t = 0.5, 1, and 3. (3 marks)

d. Estimate Pauls regular contributions while he has fully paid the mortgage at t = 3.5, 4, . and 11.5. (3 marks)