Are you smarter than a year 12 student?
I recently presented a personal finance assignment given to year 12 students and here is one reader’s attempt at answering the question.
Last week I published an article sharing a mathematics exercise that a teacher gave to his year 12 students. I thought it was a great question which asked students to consider real-life financial decisions that many Australians face. See the original article here.
Many of the readers of the article took me up on the challenge and sent through their answers. I can’t publish them all but I did want to highlight one answer from a reader named Sandy. I’ve also added some resources for anyone who struggled coming up with an answer.
The students were given several options to define the exercise within broad parameters. Here are Sandy’s choices which will provide the basis for the calculations. Sandy’s responses are in bold and my own perspective is in italics.
Part A: Baseline Figures
Make assumptions on the values for x, y and z above using the following guidelines:
Home Loan ($x): $400k-$600k selected mid-value figure $500,000
Super Balance ($y): $40k-$80k selected mid value figure $50,000
Annual Income ($z): $80k-$120k selected mid value figure of $100,000
How much interest will Nick pay over the 30-year period? Using CBA home loan calculator?
The answer is $3,161
There are many mortgage repayment calculators available on the internet. People typically use them when they are considering a new mortgage but it is also a great way to model out different interest rate scenarios that may occur in the future.
Question 2: Calculate the monthly amount deposited into Nick’s superannuation fund by his employer net of contributions tax (15%).
$100,000 x 11.5% = $11,500 /12 = $958.33 x (1-0.15) = $814.58
Super is a tax-advantaged but not tax-free environment. Contributions are taxed at 15% instead of a marginal tax rate. Sandy calculated the contributions into super by applying 11.5% compulsory super rate to a $100,000 salary, accounting for the 15% tax and figuring out how much would be contributed monthly.
Question 3: Calculate the total amount he will save in his superannuation fund by age 60.
The final balance is $1,255,541.24 (payment beginning of month) using Casio ClassPad 330 calculator and verified by TVM Calculator.
The return is $1,255,541.24 less $50,000 = $1,205,541.24
Answer $1,255,541.24 the final balance an increase of $1,205,541.24 over the $50,000 opening balance.
A financial calculator is a great tool for investors. It allows you to calculate how much a lump sum of money and any additional contributions will grow to given returns over different periods of time. This is useful because you can model out how different decisions like how much you save and how long you save will impact the wealth you build over the long-term.
There are some nuances to financial calculators and each is a bit different. In the one selected by Sandy we can see several terms that may confuse some readers. Here are some tips:
- The mode section allows a user to select beginning of the period or the end of the period. In this case with a monthly payment this would indicate the investment occurring at the beginning of the month or the end of the month.
- It is important to match the frequency of the payments with the number of periods involved. In this case the contribution to super is monthly so Sandy has listed the periods as months – 360 months indicating 30 years.
- The future value figure is negative which may confuse some readers. This is a quirk of financial calculators. Technically any cash flow invested is a negative cash flow as you are taking cash and putting it into an investment. The current investment of $50,000 and each of the contributions should have been negative numbers which would make the future value positive. In practical terms this is irrelevant as long as you know the negative value should be thought of as a positive number.
- This calculator allows a user to select the compounding period. Compounding is earning a return on a return. The more frequent the compounding the higher the total amount would be at the end. Generally, we think about share market returns on an annual basis so I would just suggest you use annual. That is the most conservative option to select.
Financial calculators also allow you to calculate the return you need to achieve a goal given a time frame and certain levels of saving. You can solve for any variable in the time value of money formula. Some calculators allow you to take inflation into account.
I think every investor would benefit from spending some time with a financial calculator. Understanding how differences in savings rates, returns and time impact wealth generation are invaluable. I’ve tried to outline some of the lesson in the following two articles:
Sandy assumed that there would be no salary increases. It is unlikely that Nick would not receive a salary increase over his career and there is an intention to continue to increase the compulsory super rate in the coming years. However, salary increases are difficult to model over a career. In real life you can re-run the model if, and when, salary increases are received and re-adjust retirement assumptions.
Part B: Tax Cuts Prediction
Use the Stage 3 tax cuts calculator to calculate Nick’s annual tax savings.
Convert this to a monthly amount that Nick can use to either boost his superannuation savings or pay down his mortgage.
The tax cut for a person earning $100,000 is $2,179 per annum or $181.58 per month.
This one is straightforward. I don’t have much to add.
Question 4: Make a prediction as to which option (boost superannuation savings or pay down the mortgage) will put Nick in the strongest financial position when he retires at age 60.
OPTION 1
Add the tax savings to superannuation the new accumulated superannuation balance would assuming no salary increase over 30 years would be:
$1,457,489.05
This is an increase of $ 201,947.81 ($1,457,489.05 - $1,255,541.24) assuming that the tax savings is contributed as a Non-Concessional Contribution therefore not attracting the 15% contributions tax.
In this case the decision was made to treat the contribution as a non-concessional contribution. A non-concessional contribution is an after-tax contribution. The full marginal tax rate is paid on income and the contribution is then made to super. This differs from a concessional contribution which is made pre-tax and is subject to a tax rate of 15% when contributed to super.
The concessional cap currently is $30,000 so technically at a $100,000 salary the full cap would not be hit with a 11.50% compulsory super rate. However, I understand this assumption because a salary should increase over time and the concessional cap will increase which makes the exact impact difficult to model. I think this is a conservative way to model out the lifetime impact of the tax savings.
OPTION 2
Add the tax savings to the mortgage repayment.
This option reduces the interest paid on the mortgage to $528,537 compared to the previous scenario where the interest payable was $637,723 a savings of $109,186.
This option would result in a savings of $109,186.
Pre-paying a mortgage accelerates the amortisation schedule of a mortgage and reduces the interest paid to the bank. For more on how mortgages work and considerations for investors see the following article:
However, to provide an accurate assessment of Nick’s financial position at age 60 the following approach is examined.
Option 1
The superannuation balance after 30 years assuming the SGC (Superannuation Guarantee Charge less 15% tax) and the tax savings is contributed:
The resulting sum is $1,457,489.05 as was calculated in question 4 option 1.
Option 2
As the housing loan is paid off 4.3 years (54 months) earlier if the tax savings is contributed to the loan repayments.
This allows another calculation to be made:
Superannuation balance with for 54 months with tax savings plus the normal loan repayment.
Step 1
The superannuation balance assuming the SGC contribution is made less 15% tax as per question 1.
The resulting sum is $1,255,541.24 as per question 2 calculation.
Step 2
Calculate superannuation accumulated for 54 months contributing the housing loan repayment $3,161 plus the tax savings $181.58 that is a total of $3,342.58.
The accumulated sum is $210,150.78
The total superannuation balance would be $1,255,541.24 + $210,150.78 = $1,465,692.02
This provides a higher accumulated sum that the previous option: $1,465,692.02 less $1,457,489.05 = $8,202.97
Earlier Sandy calculated the impact of the interest savings from making additional mortgage payments. That is an undeniable benefit from making extra mortgage payments. The extra mortgage payments also allow Nick to pay off his mortgage early. Having a fully paid off home is one of the best things that can happen for someone from a personal finance perspective.
The price of housing in Australia is well documented and it means that for many people a mortgage payment is by far the largest expense. Getting rid of that expense is a significant milestone on the journey to financial independence. In this case Sandy has assumed that mortgage payments have been redirected to super.
Question 5: Explain the reasoning behind the formation of your prediction.
As the interest rate on the loan and the superannuation growth rate is the same 6.5% and the term is the same 30 years the outcome would be very similar. This proved to be the case.
Directing the tax savings to the loan proved to provide a better outcome. This is due to the loan being paid 4.3 years (54 months) earlier.
This allowed the normal loan instalments to be contributed to superannuation for 54 months. This strategy led to a $8,202.97 better outcome.
Anytime you model out a scenario like this it is important to understand the impact of any of your estimates or assumptions changing. If the assumptions that the super contributions are non-concessional is not accurate it may tip the balance to super’s advantage. If the return earned on super is higher than 6.5% that option will result in more wealth. If interest rates go down and the interest on the mortgage is less than 6.5% over the life of the loan the super option also may be the best choice. If returns are lower and interest rates are higher paying off the mortgage will be even more advantageous.
Final thoughts
What I liked so much about this question is that it dealt with financial decisions that millions of Australians face. What to do with tax cuts? Should you invest or pay off your mortgage? How much money will you have at retirement?
I will reiterate a point I made in the first article introducing the exercise. Being able to do the maths behind the decisions we make with our money matters. The first step before making any decision is to understand the impact of that decision on our future outcomes.
That doesn’t mean you will - or should - simply choose the path that likely results in the largest gain in your net worth over time. We all will make different trade-offs based on our individual goals, our temperaments and the need to be able to sleep at night. But to make an informed decision requires understand the real trade-offs we are making which means calculating the impact of different decisions.
The inescapable truth is that financial literacy requires numerical literacy. The good news is that you don’t have to do any of the calculations yourself. There are numerous free calculators and tools available on the internet. What is far more important is to understand directionally the drivers of amassing wealth.
Returns matter and that is often our focus in the investment industry. But far more important are the things that you can control – time and the amount you save. That is why it is so important that the lessons from this exercise are learned early. Something that one group of year 12 students is fortunate to get as part of their high school curriculum.
Feel free to share your thoughts with me at [email protected]
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