1. Modelling with Mathematics
Number: Revision questions

2. Clarify
Jordan told me that she thinks investing in shares is more risky than investing in a term deposit bank account.
What does risky mean in this context?
Explain why investing in shares might be risky.
What would Jordan need to do to be able to compare how an investment in shares compares with a bank term deposit?

3. Clarify - answers
Risky means that the investment might actually lose money instead of making a profit.
Shares are worth what people are willing to pay for them. That in turn depends on how successful the company is. If a company has problems its share price is likely to go down. In the worst case, if a company goes broke, the shares would become worthless and you would lose all your investment.

4. Clarify - answers
To compare an investment in shares with a term deposit, Jordan would need to
Decide on the term of the investment;
Calculate the compound interest for the term deposit for the term of the investment;
Choose shares to invest in and use the historical value of the shares to work out what profit she would have made on the shares, taking into account brokerage.
Historical values gives an indication of how the share prices are likely to change, but there is no guarantee that future prices will behave in the same way.

5. Choose
Write the steps that you would follow to determine the total cost of an interest only fixed-interest loan of $ over 15 years at 7.25% p.a.
Assume a loan application fee of $1 800.
Assume stamp duty of 0.3% of the principal.
Note: an interest only loan is one where you pay the interest each month and the principal is repaid in full at the end of the loan.
Make sure to full include details of any calculations needed.

6. Choose - answers
An interest-only loan is effectively simple interest, as the principal does not change, so use the Simple Interest formula SI=P x R/100 x T = x 7.25/100 x15.
Stamp duty is based on the amount of the loan, so it comes to SD = 0.3/100 x
Add the Simple Interest, Stamp Duty and Loan Application Fee to get the total cost: Cost = SI + SD

7. Use Calculate the total cost of the interest only loan with:
Principal (P) = $
Interest Rate (R) = 7.25%
Time (T) = 15 years
Loan Application Fee = $1800
Stamp duty = 0.3% of the principal
Assume that the loan application fee and stamp duty are paid at the beginning of the loan, and the interest is paid every month. Calculate the monthly interest payment. (Use the simple interest formula.)

8. Use - answers Cost Monthly payment
SI=P x R/100 x T = x 7.25/100 x =
SD = 0.3/100 x = 750
Cost = =
Monthly payment
SI = P x R/100 x T = x 7.25/100 x 1/ = $ per month

9. Interpret/Check
Jarryd did the following calculations to compare the cost of two loans for $5000:
Based on Jarryd’s calculations, what would you recommend?
Are Jarryd’s calculations correct?
Loan A
Loan B
Rate
18.5%
16.8%
Interest
$840
$925
Fees $0
$250
Total
$1175

10. Interpret/Check answers
Based on Jarryd’s calculations, loan B is much more expensive than loan A. Jarryd should go with loan A.
There’s something wrong with Jarryd’s calculations. Loan B has a lower interest rate than loan A but Jarryd has calculated more interest for loan B. That can’t be right.