Using a Future Value Table Revision Notes for HSC SSCE Mathematics Standard

Using a Future Value Table

What is a future value table?

A future value table is a practical tool that simplifies annuity calculations. Instead of using complex formulas repeatedly, the table provides pre-calculated values that show what $1 will grow to when invested regularly over different time periods at various interest rates.

The table shows the future value of an annuity where $1 is invested at the end of each period, with interest compounded per period. These pre-calculated values act as multiplication factors that you can use with your actual investment amount.

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For example, if you look up the value for 6 periods at 6% interest per period, you'll find 6.9753. This means that investing $1 at the end of each period for 6 periods at 6% interest will grow to $6.9753.

Understanding the future value table structure

Future value tables are organized in a grid format:

Rows represent the number of time periods (such as years, months, or quarters)
Columns represent the interest rate per period (as a percentage)
Intersection values are the multiplication factors you'll use in your calculations

Here is an example of a future value table:

Period	1%	2%	3%	4%	5%	6%
1	1.0000	1.0000	1.0000	1.0000	1.0000	1.0000
2	2.0100	2.0200	2.0300	2.0400	2.0500	2.0600
3	3.0301	3.0604	3.0909	3.1216	3.1525	3.1836
4	4.0604	4.1216	4.1836	4.2465	4.3101	4.3746
5	5.1010	5.2040	5.3091	5.4163	5.5256	5.6371
6	6.1520	6.3081	6.4684	6.6330	6.8019	6.9753

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Key point: The intersection value includes both the total of all your contributions AND the compound interest earned. This is why the value for period 1 is always 1.0000 (no interest has been earned yet on a single contribution).

Steps to use a future value table

Follow these three steps when working with future value tables:

Step 1: Identify the number of time periods and the interest rate per period

Step 2: Find where the period row and interest rate column meet in the table (the intersection value)

Step 3: Multiply the intersection value by the regular contribution amount

Adjusting for different compounding frequencies

When interest is compounded more frequently than annually, you must adjust both the number of periods and the interest rate:

Number of periods: $n = \text{number of years} \times \text{compounding frequency per year}$

Interest rate per period: $r = \frac{\text{annual interest rate}}{\text{compounding frequency per year}}$

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Common compounding frequencies:

Annually: 1 time per year (no adjustment needed)
Semi-annually (six-monthly): 2 times per year
Quarterly: 4 times per year
Monthly: 12 times per year
Biannually: 2 times per year (same as semi-annually)

chatImportant

Always check whether the interest rate given is per annum (p.a.) or per period. If it's per annum and compounding is more frequent than yearly, you must divide the rate by the compounding frequency.

Calculating future value

To calculate the future value of regular contributions, use this formula:

$FV = \text{intersection value} \times \text{contribution amount}$

Where:

$FV$ = future value of the annuity
Intersection value = the number from the table
Contribution amount = the regular payment made each period

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Worked Example 1: Annual compounding

Question: Calculate the future value of $34,000 invested per year for 3 years at 5% p.a. compounded annually.

Solution:

Identify the period: $n = 3$ years
Identify the interest rate: $r = 5\%$ per year
Find the intersection value from the table for period 3 and interest rate 5%
Intersection value is $3.1525$
Apply the formula:

$FV = 3.1525 \times 34000$

$FV = 107185$

Answer: The future value is $107,185

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Worked Example 2: Six-monthly compounding

Question: Calculate the future value of $5,000 invested per half-year for 2 years at 6% p.a. compounded six-monthly.

Solution:

Calculate the number of periods: $n = 2 \times 2 = 4$ (2 years × 2 periods per year)
Calculate the interest rate per period: $r = \frac{6}{2} = 3\%$ per half-year
Find the intersection value from the table for period 4 and interest rate 3%
Intersection value is $4.1836$
Apply the formula:

$FV = 4.1836 \times 5000$

$FV = 20918$

Answer: The future value is $20,918

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Worked Example 3: Monthly compounding

Question: What is the future value of an investment of $300 per month for 3 months at 24% p.a. compounded monthly?

Solution:

Using this future value table:

Period	1.0%	1.5%	2.0%	2.5%	3.0%	3.5%	4.0%
1	1.000	1.000	1.000	1.000	1.000	1.000	1.000
2	2.010	2.015	2.020	2.025	2.030	2.035	2.040
3	3.030	3.045	3.060	3.076	3.091	3.106	3.122
4	4.060	4.091	4.122	4.153	4.184	4.215	4.246

Number of periods: $n = 3$ months
Interest rate per period: $r = \frac{24}{12} = 2\%$ per month
Find the intersection value for period 3 and interest rate 2%
Intersection value is $3.060$
Apply the formula:

$FV = 3.060 \times 300$

$FV = 918$

Answer: The future value is $918

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Worked Example 4: Quarterly compounding

Question: What is the future value of an investment of $15,000 per quarter for 1 year at 12% p.a. compounded quarterly?

Solution:

Number of periods: $n = 4 \times 1 = 4$ (1 year × 4 quarters per year)
Interest rate per period: $r = \frac{12}{4} = 3\%$ per quarter
Find the intersection value for period 4 and interest rate 3%
Intersection value is $4.184$
Apply the formula:

$FV = 4.184 \times 15000$

$FV = 62760$

Answer: The future value is $62,760

Finding the payment or contribution amount

Sometimes you know the desired future value and need to find what regular payment is required. This is a reverse calculation where you rearrange the formula:

$\text{PMT} = \frac{FV}{\text{intersection value}}$

Where:

$\text{PMT}$ = payment or contribution per period
$FV$ = desired future value
Intersection value = the number from the table

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Worked Example 5: Finding annual payment

Question: Find the payment per period of an annuity with a future value of $76,713 at 3.5% p.a. compounded annually for 4 years.

Solution:

Number of periods: $n = 4$ years
Interest rate: $r = 3.5\%$ per year
Find the intersection value for period 4 and interest rate 3.5%
Intersection value is $4.215$
Set up the equation:

$FV = 4.215 \times \text{PMT}$

$76713 = 4.215 \times \text{PMT}$

Divide both sides by the intersection value:

$\frac{76713}{4.215} = \text{PMT}$

$\text{PMT} = 18200$

Answer: The payment required is $18,200 per year

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Worked Example 6: Finding biannual payment

Question: Find the payment per period of an annuity with a future value of $6,105 at 7% p.a. compounded biannually for 1 year.

Solution:

Number of periods: $n = 2 \times 1 = 2$ (1 year × 2 periods per year)
Interest rate per period: $r = \frac{7}{2} = 3.5\%$ per period
Find the intersection value for period 2 and interest rate 3.5%
Intersection value is $2.035$
Set up the equation:

$6105 = 2.035 \times \text{PMT}$

Divide both sides by the intersection value:

$\frac{6105}{2.035} = \text{PMT}$

$\text{PMT} = 3000$

Answer: The payment required is $3,000 per half-year

chatImportant

When finding the payment amount, always check your answer makes sense. The total of all payments should be less than the future value (because the future value includes interest earned).

bookmarkSummary

Key Points to Remember:

Future value tables simplify annuity calculations by providing pre-calculated multiplication factors for $1 invested regularly
To use the table: identify the period and interest rate, find the intersection value, then multiply by the contribution amount
When compounding occurs more frequently than annually, adjust both the number of periods (multiply by frequency) and the interest rate (divide by frequency)
To calculate future value: $FV = \text{intersection value} \times \text{contribution}$
To find the required payment: $\text{PMT} = \frac{FV}{\text{intersection value}}$
Always ensure your period count and interest rate match the compounding frequency specified in the question

Using a Future Value Table (HSC SSCE Mathematics Standard): Revision Notes