SQA Higher Applications of Mathematics Finance: present and future value, loans and credit, tax, inflation and insurance

What Finance actually demands

Finance carries the largest weighting in the question paper, roughly $30$ to $45$ per cent, so it rewards solid effort. The examiners test whether you can grow and discount money correctly, track borrowing, and apply tax, inflation and insurance to real planning decisions. Many questions use a spreadsheet, so the modelling and technology skills from the first area feed straight in. This guide ties together the three dot-point pages of the module.

Present and future value

The core idea is the time value of money: a sum grows under compound interest, so money now is worth more than the same money later. The future value of a lump sum is $\text{FV} = \text{PV} \times (1 + i)^{n}$, and the present value of a future amount reverses this as $\text{PV} = \dfrac{\text{FV}}{(1 + i)^{n}}$. Compounding more often than yearly raises the effective annual rate $\left(1 + \dfrac{r}{m}\right)^{m} - 1$, which is why products must be compared on an effective basis, not by headline rates. Regular savings are modelled period by period, each deposit growing for the time it is invested.

Loans, credit and APR

Borrowing reverses saving: a balance grows by interest each period and falls by each repayment, so the rule is new balance $= (\text{old balance} \times (1 + i)) - \text{payment}$. A credit card charges interest on the unpaid balance, so paying only the minimum lets debt compound, while clearing the balance in full is interest-free. The annual percentage rate (APR) expresses the true yearly cost of credit including compounding, letting you compare products fairly; convert a monthly rate to an effective annual rate with $\left(1 + i\right)^{12} - 1$ before comparing, and judge a loan by the total repaid, not just the monthly payment.

Financial planning: tax, inflation and insurance

Income tax is charged only on income above a tax-free allowance, often in rising bands, and national insurance is a further deduction. Inflation raises prices, so a fixed cash sum loses real value: its purchasing power after $n$ years is $\dfrac{\text{amount}}{(1 + r)^{n}}$ in today's prices, and savings must beat inflation to hold their value. Insurance trades a known premium for protection against an uncertain loss, with an excess paid on each claim; the premium reflects the risk, and insurers price it using expected value from the probability area.

How Finance is examined

A typical SQA profile for this area:

• Growing and discounting. Future and present value, and comparing savings products by effective rate.
• Borrowing. Loan balances month by month, credit cards, and comparing options by APR.
• Planning. Income tax and national insurance, take-home pay.
• Real value and protection. Inflation and purchasing power, and insurance premiums, excess and risk.

Check your knowledge

A mix of recall and method questions covering the module. Attempt them, then check against the solutions.

1. Find the value of $\pounds 2000$ after $2$ years at $5\%$ compounded annually. (2 marks)
2. How much must you invest now at $4\%$ to have $\pounds 3000$ in $3$ years? (2 marks)
3. A $\pounds 1000$ loan at $2\%$ per month has a $\pounds 300$ payment. Find the balance after one payment. (2 marks)
4. A worker earns $\pounds 20\,000$ with a $\pounds 12\,570$ allowance and $20\%$ rate. Find the income tax. (2 marks)
5. A $\pounds 100$ item rises with $5\%$ inflation. Find its price after one year. (1 mark)