Question 1: A bill of exchange with a face value of $100,000 and 120 days to maturity was taken out on 15 July 2014 at simple interest of 7.2% p.a. If the bill was subsequently sold on 30 September 2014 at a simple interest rate of 6.8% p.a.
(a) What was the % p.a. rate of simple interest earned by the seller for the period?
(b) What was the effective interest rate earned by the seller?
Draw appropriate time-line(s) to demonstrate your calculations.
Question 2: You have decided to purchase a small apartment hence are actively looking for different loan options. You notice some lenders are encouraging borrowers to repay their loans with weekly payments, instead of with payments at the end of each month. One of these lenders recently advertised:
"If you divide the normal monthly loan payment by 4 and pay this amount weekly, you will reduce the term of your loan and thereby reap big reductions in the cost of your loan".
(a) For a 15 year loan to borrow $245,000 with interest charged daily at an interest rate of 6.5% p.a. use financial maths only (not an amortisation schedule) to demonstrate the effect on the term of the loan if a borrower takes the weekly payment alternative. Draw appropriate time-lines to demonstrate your calculations.
(b) Discuss whether it is correct for the advertisement to say that the weekly repayments will result in ‘big reductions in the cost of your loan'.
Question 3: You are considering investing in Commonwealth Bonds and have found the following information about them from the financial press in the middle of March 2014:
Coupon rate (%) Maturity Coupon dates Price ($) Yield
8.0 August 2016 15th February, 103.36 6.75
15th August
By the time you make up your mind to purchase these bonds on 10 April 2014, the Reserve Bank has reduced interest rates and the yield has fallen to 6.25%.
(a) Draw appropriate time-line to demonstrate your calculations.
(b) What price will you have to pay for the bond?
(c) What are the various components of the price paid by you?
(d) Prepare an amortisation schedule for the remaining term of the bond till maturity.
(e) If you subsequently sold the bond on 6 July 2015 for a yield of 8.15%, what are the components of your sale proceeds?
Question 4: Recently, Fusspot Electronics advertised a Sunny Handycam Video recorder, which has a normal cash price of $1,988, under a rental/purchase scheme for 36 payments of $73.61 per month, the first such payment being due on the date when the contract is signed. A condition of the contract is that the purchaser must take out a service agreement as soon as the warranty of 12 months expires - this agreement can be obtained by paying $80 now or $4 per month when the warranty has expired.
As an alternative, you can pay $25 to join Shonky Credit Union and obtain the funds to pay the cash price of the Video recorder. Shonky Credit Union advertises its consumer loans with the example of "borrow $5,000 at the low simple interest rate of 12% p.a. with repayments of only $258.33 per month". This alternative will enable you to avoid the compulsory service agreement but, if you wish to cover the system, you can enter a service agreement with Electronic Maintenance Co for $35 per annum payable at the beginning of the relevant years.
REQURIED:
Evaluate each of the alternatives to obtain the Handycam and recommend which alternative should be used. Ensure that your evaluation is comparing "like" with "like" alternatives. Draw appropriate timelines to demonstrate your calculations.