Leaving Cert Financial Maths (Higher Level): Compound Interest, AER & Amortisation

Financial maths applies sequences and series to money: compound interest, AER, present value, annuities and loan amortisation. It is examined on Paper 1.

Written by Sean Doyle · Last updated: 2026-06-12

Key facts

Compound interest uses the formula F = P(1 + i)^t.
AER (annual equivalent rate) lets you compare interest rates fairly.
Present value works backwards to find what future payments are worth today.
Amortisation questions (loans and mortgages) use the geometric series formula.

Financial Mathematics explained

What is Present Value?

Present Value (PV) is the current worth of a future sum of money.

Key concept: Money today is worth more than the same amount in the future because: - It can earn interest - Inflation reduces purchasing power - Opportunity cost of waiting

Example: Would you rather have €100 today or €100 in 1 year? Answer: €100 today! You could invest it and have more than €100 in a year.

Present value calculates: "What amount today equals a future amount?"

Present Value Formula

The present value formula is:

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

Where: - PV = Present Value (amount today) - FV = Future Value (amount in the future) - r = Interest rate per period (as a decimal) - n = Number of periods

Rearranged for Future Value: $\text{FV} = \text{PV}(1+r)^n$

This is the compound interest formula!

Discount Rate and Time Value

Discount rate is the interest rate used to find present value. It represents the "cost" of waiting.

Effects of changing variables: - Higher interest rate → Lower PV (future money worth less today) - Longer time period → Lower PV (more time for discounting) - Higher future value → Higher PV (more money = more value)

Practical uses: - Investment decisions - Loan valuations - Pension planning - Business project evaluation

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Key formulas

Name	Formula	Description
Simple Interest	$I = Prt$	Interest = Principal × rate × time
Compound Interest	$A = P(1 + r)^t$	Amount after t periods with compound interest
Present Value	$P = \frac{F}{(1+r)^t}$	Present value of future amount F
Depreciation	$V = P(1 - r)^t$	Value after depreciation at rate r
Amortisation	$A = P \cdot \frac{r(1+r)^n}{(1+r)^n - 1}$	Regular payment to repay loan
Annuity (Future Value)	$FV = P \cdot \frac{(1+r)^n - 1}{r}$	Future value of regular payments

Worked examples

Worked example 1

What is the present value of €8,000 in 4 years at 6% interest?

Using PV = FV/(1+r)^n: PV = 8000/(1.06)^4 = 8000/1.2625 = €6,336.75

Answer:

€6,336.75

Worked example 2

What is €2,000 worth after 5 years at 4% annual compound interest?

Using A = P(1+r)^n: A = 2000(1.04)^5 = 2000(1.2167) = €2,433.31

Answer:

€2,433.31

Where students lose marks

Using the nominal rate instead of converting to the correct period rate.
Rounding too early and losing accuracy in the final euro amount.
Confusing present value and future value.

Frequently asked questions

What is the compound interest formula for the Leaving Cert?

Final value F = P(1 + i)^t, where P is the principal, i is the rate per period as a decimal, and t is the number of periods.

How are loans and mortgages examined?

Loan and mortgage questions use amortisation, which combines present value with the geometric series formula to work out repayments.

Is financial maths on Paper 1?

Yes, financial maths is examined on Paper 1 of Leaving Cert Higher Maths.

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