Present/future value | Year 11

01 / LEARN

The idea, step by step

Move along a time line

For one payment, $F V = P V {(1 + i)}^{n}$ . To find a required current deposit, rearrange to $P V = F V / {(1 + i)}^{n}$ . Mark the deposit date as period 0 and the target date as period $n$ .

Do not use the number printed on a calendar date as the period count. A deposit at the end of Year 1 valued at the end of Year 4 earns three annual periods.

Interpret present value

For a positive rate, present value is below future value because the initial sum earns interest. Reverse compounding by division, not by subtracting simple interest.

If a minimum deposit must meet a target, round the computed deposit upward to cents and verify it. Ordinary nearest-cent rounding can produce a small shortfall.

A common trap

Discount future value by subtracting rate×time.

Instead: Divide by the complete compound growth factor.

02 / WORKED EXAMPLES

See the thinking

Example 1

Worked example

Find the minimum deposit for AUD 5000 in 3 years at 4% annually.

PV=5000/(1.04)^3=4444.981793.
Round upward to cents so its future value is at least 5000.

AUD 4,444.99

Example 2

Worked example

Value AUD 3500 after 2 years at 5% nominal compounded quarterly.

i=0.0125;n=8.
FV=3500(1.0125)^8.

AUD 3,865.70

Check your understanding

Present value of AUD 1210 in 2 years at 10% annually?

Show answer

AUD 1,000.00

1210/(1.1)^2=1000.

03 / WORKSHEET

Your turn

6 questions · 12 marks · Work at your own pace.

Worksheet PDF Worked solutions

Read the questions online

Future value of AUD 2400 at 3% annually for 4 years?
2 marks
Present value of AUD 6000 in 2 years at 5% annually, nearest cent?
2 marks
Minimum deposit for AUD 8000 in 5 years at 6% annually?
2 marks
An investment reaches AUD 5500 after 8 quarters at 1.2% per quarter. Find the starting sum.
2 marks
For a fixed positive rate and future target, why does a longer term need less starting money?
2 marks
Count annual periods from the end of Year 1 to the end of Year 4.
2 marks

Read the worked solutions

Equivalent correct methods earn the corresponding marks. Include units where asked.

Future value of AUD 2400 at 3% annually for 4 years?
2 marks
2400(1.03)^4.
AUD 2,701.22
Present value of AUD 6000 in 2 years at 5% annually, nearest cent?
2 marks
6000/(1.05)^2.
AUD 5,442.18
Minimum deposit for AUD 8000 in 5 years at 6% annually?
2 marks
8000/(1.06)^5=5978.065383.
Round up to cents.
AUD 5,978.07
An investment reaches AUD 5500 after 8 quarters at 1.2% per quarter. Find the starting sum.
2 marks
PV=5500/(1.012)^8.
AUD 4,999.41
For a fixed positive rate and future target, why does a longer term need less starting money?
2 marks
PV=FV/(1+i)^n; increasing n increases the denominator.
The larger growth factor produces a smaller present value.
Count annual periods from the end of Year 1 to the end of Year 4.
2 marks
The intervals are 1→2,2→3,3→4.
3

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Curriculum reference & lesson scope

SACE Board of South Australia

Stage 1 General Mathematics: investing and borrowing. Supplied educational models cover interest, investment comparisons, shares and credit; they are not recommendations of real products or statements of personal tax liability.

Official curriculum source ↗

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