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Investment: simple and compound interest, future and present value, inflation and shares: HSC Maths Standard 1 Year 12

Syllabus dot point

“Calculate and compare the value of different types of investments over time, including simple interest, compound interest (future value and present value, with interest rates other than per annum), the effect of inflation, and investing in shares (dividends and dividend yield)”

HSCMaths Standard 1Year 12: Financial Mathematics8 min read

Quick answer

Simple interest I=PrnI = Prn grows linearly; compound interest FV=PV(1+r)nFV = PV(1 + r)^n grows exponentially, using the rate per period and the number of periods. Present value PV=FV÷(1+r)nPV = FV \div (1 + r)^n finds the amount to invest now. Inflation raises prices by compounding, and shares earn dividends (yield = dividend ÷ price) but carry the risk of price changes.

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  1. What this dot point is asking
  2. The answer
  3. Practice questions

What this dot point is asking

You need to calculate and compare investment returns: simple interest, compound interest (including different compounding periods), present value, the effect of inflation, and share investments. NESA's topic guide notes that interest calculations should include rates expressed other than per annum.

The answer

Simple interest

I=PrnI = Prn

Interest is calculated only on the original principal, so it grows by the same amount each period (a linear graph).

Compound interest (future value)

FV=PV(1+r)nFV = PV(1 + r)^n

  • rr is the interest rate per compounding period; nn is the number of periods.
  • Monthly: divide the annual rate by 12 and multiply years by 12; quarterly: 4; half-yearly: 2.
  • Interest =FV−PV= FV - PV.
  • Compound growth is exponential: interest earns interest.

Present value

PV=FV(1+r)nPV = \frac{FV}{(1 + r)^n}

This finds how much to invest now to reach a target, for example saving for a car.

Tables of compounded values of $1 can also be used: multiply the principal by the table value for the rate and number of periods.

Inflation

Inflation increases prices over time. Use the compound interest formula with the inflation rate to predict future prices, and compare investment returns with inflation to judge real growth.

Shares

Share vocabulary
  • Share: part-ownership of a company, bought at the market price.
  • Dividend: a payment to shareholders, usually per share.
  • Dividend yield =dividend per shareshare price×100%= \frac{\text{dividend per share}}{\text{share price}} \times 100\%.
  • Shares can rise or fall in value and dividends are not guaranteed; brokerage fees may apply.
Worked example

How much must be invested now at 3% p.a. compounded quarterly to have $10 000 in 5 years?

  1. r=0.034=0.0075r = \frac{0.03}{4} = 0.0075, n=20n = 20.
  2. PV=10 000(1.0075)20=10 0001.161184=$8611.90PV = \frac{10\,000}{(1.0075)^{20}} = \frac{10\,000}{1.161184} = \$8611.90.
Common traps
Using the annual rate with monthly periods
Divide the rate and multiply the time by the same number.
Adding simple and compound interest ideas
Compound interest recalculates on the growing balance.
Ignoring risk with shares
Returns are not guaranteed.

Practice questions

Original practice questions graded from foundation to exam level, each with a full worked solution. Try them before revealing the solution.

foundation3 marks
Find the simple interest on 4000 dollars at 3.5% p.a. for 3 years, and the total value.
Show worked solution →

I=Prn=4000×0.035×3=$420I = Prn = 4000 \times 0.035 \times 3 = \$420.

Total value =4000+420=$4420= 4000 + 420 = \$4420.

Marking guide: 1 mark for substitution, 1 mark for the interest, 1 mark for the total.

core4 marks
Leah invests 6000 dollars at 4.8% p.a. compounded monthly for 5 years. Find the future value and the interest earned.
Show worked solution →

r=0.04812=0.004r = \frac{0.048}{12} = 0.004, n=5×12=60n = 5 \times 12 = 60.

FV=6000(1.004)60=6000×1.27064=$7623.84FV = 6000(1.004)^{60} = 6000 \times 1.27064 = \$7623.84 (to the nearest cent, using the calculator value).

Interest =7623.84−6000=$1623.84= 7623.84 - 6000 = \$1623.84.

Marking guide: 1 mark for r, 1 mark for n, 1 mark for FV, 1 mark for interest.

exam5 marks
Sam has 5000 dollars to invest for 4 years. Option A: a term deposit at 4.2% p.a. compounded quarterly. Option B: 400 shares at 12.50 dollars each, which pay an annual dividend of 0.60 dollars per share (assume the share price stays the same and dividends are not reinvested). Compare the options and state one risk of Option B.
Show worked solution →
Option A
r=0.0424=0.0105r = \frac{0.042}{4} = 0.0105, n=16n = 16. FV=5000(1.0105)16=5000×1.18190=$5909.50FV = 5000(1.0105)^{16} = 5000 \times 1.18190 = \$5909.50. Interest about $909.50.
Option B
dividends per year =400×$0.60=$240= 400 \times \$0.60 = \$240; over 4 years =$960= \$960. Dividend yield =0.6012.50×100%=4.8%= \frac{0.60}{12.50} \times 100\% = 4.8\%. Value after 4 years =$5000+$960=$5960= \$5000 + \$960 = \$5960 (if the price is unchanged).
Comparison
Option B earns slightly more ($960 against about $909.50), but only if the share price holds and dividends continue.
Risk
share prices can fall and dividends can be cut, so Sam could lose money, while the term deposit's return is guaranteed.

Marking guide: 2 marks for Option A, 2 marks for Option B, 1 mark for comparison with a risk.

Practise this

Sources & how we know this

Based on the official NESA syllabus. Not yet individually reviewed by a person; always check NESA and your school's materials for current rules.

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