please answer each question and show the working step

ACST201 Financial Modelling Take Home Quiz 1 S2 2017 Take Home Quiz 1 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 30year 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? End The deadline of Take Home Quiz 1 submission is August 23th 2017, 9:00AM. You need to submit your solutions (in one PDF file) to the link on iLearn to complete the submission part of this assessment. It can be typed or handwritten and scanned. You need to show the working steps in your solution. Please refer to the Assessment submission guide on iLearn for submission introduction. 2