1. Today is 1 January 2017. Jack is 25 years old today and he is planning to
purchase a house with the price of $1,000,000 when he is 35 years old (i.e., 1
Jan 2027). Jack believes that, at the time of purchasing the house, he should
have saved 20% of the house price (i.e., $200,000) over the period from 2017
to 2026) and can borrow 80% of the house price (i.e., $800,000) through a 30-
year mortgage (it starts from 1 Jan 2027) from MQ Bank at an interest rate
of j1 = 5% p.a. He will make 30 annual repayments and the first payment will
be at the end of the first year of the mortgage period (i.e., at the end of 2027).
According to the loan agreement, Jack’s repayments will be interest-only1
for
the first five years (i.e., first five payments will be interest-only payments),
followed by payments of principal plus interest for the following 25 years. This
loan needs to be fully repaid by the end of 30 years (i.e., when Jack is 65 years
old) (20 marks).
Table 1: Yield rates
2017–2022 j1 = 5.6% p.a.
2023–2026 j1 = 5.9% p.a.
(a) [2 marks] How much will Jack need to pay for the mortgage at the end
of 2027?
(b) [4 marks] After the interest-only period (i.e., first five years), what is
Jack’s annual payment amount (rounded to four decimal places)?
(c) [4 marks] Draw a carefully labelled cash flow diagram to represent the
above financial transactions from Jack’s perspective.
(d) [5 marks] After the interest-only period, assume that Jack will want
to switch the annual payment (which is paid at the end of each year)
to a monthly payment which is paid at the end of each month. What
is the equivalent effective monthly rate (expressed as a percentage and
rounded to four decimal places)? What is the equivalent monthly payment
(rounded to four decimal places)?
1
Interest-only repayment means your repayments only cover the interest on the amount you
have borrowed, during the interest-only period.
1
ACST201 Financial Modelling Take Home Quiz 1 S2 2017
(e) [5 marks] To save the 20% of the house price (i.e., $200,000), Jack plans to
deposit z% of his annual salary into a fund at beginning of each year from
2017 to 2026 (10 deposits in total). The fund return rates are assumed to
take the values in table 1. Assume that Jack’s salary is $80,000 p.a. Find
the value of z (expressed as a percentage and rounded to two decimal
places).
2. Luke wants to donate money to establish a fund to provide an annual scholarship
in perpetuity. The fund will earn an effective interest rate of 4% p.a.
and the first scholarship will be first awarded 3 years after the date of the
donation. Assume that Luke also needs to use the money from the fund to
pay for an admin fees of $1,000 at time of the donation (15 marks)
(a) [4 marks] If the amount of the annual scholarship is $41,000, what is
the required donation amount to cover all costs (rounded to two decimal
places)?
(b) [4 marks] Draw a carefully labelled cash flow diagram to represent the
above financial transactions from fund’s perspective.
(c) [4 marks] Currently, Luke has a 270-day $1,000,000 bank bill which has
been purchased 30 days ago. He wants to sell it now at a simple interest
rate to raise the money for the donation. What is the required simple
interest rate on the sale (expressed as a percentage and rounded to two
decimal places) to make this possible?
(d) [3 marks] If the bank bill in part c is sold at a simple discount rate, what
is the required simple discount rate on the sale (expressed as a percentage
and rounded to two decimal places) to make this donation possible?

 

 

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