Find the value of 1500 after 3 years at 5\% compounded annually. [2 marks]

How much must you invest now at 4\% annual to have 5000 in 5 years? [2 marks]

ScotlandApplications of MathematicsSyllabus dot point

How do you find what a sum of money is worth in the future, or what a future sum is worth today?

Calculating the future value of a sum or of regular savings under compound interest, and the present value of a future payment, including comparing savings products and the effect of compounding frequency.

A focused answer to the SQA Higher Applications of Mathematics finance content on the time value of money, covering compound interest, future value of a lump sum and of regular savings, present value of a future payment, and comparing savings products.

Generated by Claude Opus 4.810 min answerUpdated 2026-06-16

Reviewed by: AI editorial process; not yet individually human-reviewed

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What this dot point is asking
Compound interest and future value
Present value
Regular savings
Compounding frequency
Try this

What this dot point is asking

The SQA wants you to work with the time value of money: find the future value of a sum or of regular savings under compound interest, find the present value of a future payment, and compare savings products that compound at different frequencies. This is the foundation of the finance area, which carries the largest weighting in the question paper.

Compound interest and future value

Under compound interest, each period's interest is added to the balance and itself earns interest next period. The balance is multiplied by the same factor each period.

For an annual rate of $5\%$ over $3$ years, $i = 0.05$ and $n = 3$ , so the multiplier is $1.05^{3}$ . Compound growth is the same exponential model met in the modelling area, applied to money.

Find a future value

Invest $\pounds 2500$ at $4.2\%$ per year, compounded annually, for $5$ years. Find what the investment is worth at the end.

Step 1: Identify the inputs

Write down the three values the formula needs: the present value $\text{PV} = 2500$ , the interest rate per period $i = 0.042$ (converting $4.2\%$ to a decimal), and the number of periods $n = 5$ years. Naming these first prevents mistakes when substituting.

Step 2: Build the compound growth factor

Each year the balance is multiplied by $1 + i = 1.042$ . Over five years the multiplier is applied five times, giving the factor $1.042^{5}$ . This is the essence of compound interest: each year's interest itself earns interest in later years.

Step 3: Apply the formula and evaluate

\text{FV} = 2500 \times 1.042^{5} = 2500 \times 1.2285 = \pounds 3071.21

Final answer: The investment grows to $\pounds 3071.21$ , of which $\pounds 571.21$ is interest earned over the five years.

Present value

Present value answers the reverse question: how much must you invest now to reach a target amount in the future? You discount the future sum back by dividing.

Present value lets you compare amounts at different times on equal terms, which is essential for judging financial products and for the project. A larger discount rate or a longer time makes a future sum worth less today.

Find a present value

You want $\pounds 10\,000$ in $4$ years and can earn $3\%$ per year. Find how much you need to invest now.

Step 1: Recognise this as a present value question

Present value works backwards from a future target: instead of growing a sum forward, you discount it back. The formula $\text{PV} = \dfrac{\text{FV}}{(1 + i)^{n}}$ divides by the same growth factor that future value multiplies by. Identify the known values: $\text{FV} = 10000$ , $i = 0.03$ , $n = 4$ .

Step 2: Calculate the growth factor

The factor that four years of $3\%$ growth would produce is $1.03^{4} = 1.12551$ . Dividing by this factor reverses the growth and tells you what the future sum is worth today.

Step 3: Divide to find the present value

\text{PV} = \dfrac{10000}{1.03^{4}} = \dfrac{10000}{1.12551} = \pounds 8884.87

Final answer: You need to invest $\pounds 8884.87$ now. At $3\%$ per year this grows to $\pounds 10\,000$ in four years, so that future target is worth about $\pounds 8885$ in today's money.

Regular savings

Many products take a regular payment each period rather than a single lump sum. Each deposit earns compound interest for the time remaining, so the earliest deposits grow the most. A spreadsheet column models this well: each row adds the new deposit and grows the running total by the period multiplier.

Compounding frequency

Interest may compound annually, monthly or daily. The more often it compounds, the more the balance grows for the same headline rate, because interest starts earning interest sooner.

This is why a $3.95\%$ monthly account can beat a $4\%$ annual account: compounding monthly lifts the effective rate above the headline figure.

Try this

Q1. Find the value of $\pounds 1500$ after $3$ years at $5\%$ compounded annually. [2 marks]

Cue. $\text{FV} = 1500 \times 1.05^{3} = 1500 \times 1.157625 = \pounds 1736.44$ .

Q2. How much must you invest now at $4\%$ annual to have $\pounds 5000$ in $5$ years? [2 marks]

Cue. $\text{PV} = \dfrac{5000}{1.04^{5}} = \dfrac{5000}{1.21665} = \pounds 4109.64$ .

Q3. A nominal $6\%$ rate is compounded monthly. Find the effective annual rate. [2 marks]

Cue. $\left(1 + \dfrac{0.06}{12}\right)^{12} - 1 = 1.005^{12} - 1 = 0.0617$ , about $6.17\%$ .

Exam-style practice questions

Practice questions written in the style of SQA exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.

SQA Higher Apps style5 marksAmir invests

\pounds 4000

in an account paying

3.5\%

interest per year compounded annually. Find the value after

6

years, and find the present value (the amount he would need to invest now) to have

\pounds 6000

6

years at the same rate.

Show worked answer →

Future value uses the compound multiplier $1.035$ each year, so $\text{FV} = 4000 \times 1.035^{6} = 4000 \times 1.2293 = \pounds 4917.13$ (2 marks).

Present value reverses this: $\text{PV} = \dfrac{6000}{1.035^{6}} = \dfrac{6000}{1.2293} = \pounds 4880.81$ (2 marks).

So $\pounds 4880.81$ invested now grows to $\pounds 6000$ in six years at $3.5\%$ (1 mark). Markers reward the future-value multiplier raised to the correct power, dividing for present value, and rounding to the nearest penny.

SQA Higher Apps style4 marksCompare

\pounds 5000

invested at

4\%

compounded annually with the same sum at

3.95\%

compounded monthly, over one year. State which gives more and the effective annual rate of the monthly account.

Show worked answer →

The annual account gives $5000 \times 1.04 = \pounds 5200$ , a $4\%$ return (1 mark).

The monthly account applies $\dfrac{3.95\%}{12} = 0.329\%$ each month: $5000 \times \left(1 + \dfrac{0.0395}{12}\right)^{12} = 5000 \times 1.04022 = \pounds 5201.10$ (2 marks).

The effective annual rate is about $4.02\%$ , slightly more than $4\%$ , so the monthly account gives marginally more despite the lower headline rate (1 mark). Markers reward dividing the rate by $12$ , raising to the power $12$ , and comparing the effective rates.

Related dot points

Sources & how we know this

Higher Applications of Mathematics Course Specification — SQA (2023)
Higher Applications of Mathematics - Course overview — SQA (2025)