Savings - Making Your Money Work Harder
Saving means setting aside a portion of your income regularly so you can meet future goals, handle unexpected expenses, and build long-term security. The mathematics of savings is powered by percentage calculations and, over time, by the remarkable effect of compound interest.
Why Save?
- Emergency fund – covers unexpected costs such as a broken appliance or job loss. A common target is 3–6 months of essential expenses.
- Short-term goals – saving for a holiday, a car, or a new phone.
- Long-term goals – a deposit for a house, funding retirement, or building wealth.
- Security – money in savings gives you choices and reduces financial stress.
Saving Rate
Saving rate = (Amount saved ÷ Income) × 100
Financial experts often recommend saving at least 20% of your take-home income.
Even a small consistent saving rate, applied over years, builds significant wealth.
Simple Savings Growth
If you save a fixed amount each month, your total savings after n months:
Total = Monthly saving × n
This ignores interest – the next step adds that.
Interest on Savings
Simple interest: Interest = Principal × Rate × Time
Compound interest: A = P(1 + r/n)nt
Where P = principal, r = annual rate (decimal), n = compounding periods per year, t = years.
Compound interest means you earn interest on your interest – the snowball effect that makes long-term saving so powerful.
Worked Examples
Total = £150 × 36 = £5 400.
Interest = 2 000 × 0.03 × 4 = £240.
Total = £2 000 + £240 = £2 240.
A = 2 000 × (1.03)4 = 2 000 × 1.1255 = £2 251.02.
Compound interest earns £11.02 more than simple interest over 4 years – a gap that grows dramatically over longer periods.
Use the Rule of 72: approximate doubling time = 72 ÷ interest rate = 72 ÷ 6 = 12 years.
Verification: 1 000 × (1.06)12 ≈ £2 012. Close to double.
The Rule of 72
A quick mental-maths shortcut:
Doubling time (years) ≈ 72 ÷ Annual interest rate (%)
At 4%: doubles in about 18 years. At 9%: doubles in about 8 years.
This rule works because of the mathematics of exponential growth.
Types of Savings Accounts
| Account Type | Key Feature | Best For |
|---|---|---|
| Instant-access | Withdraw any time; lower interest rate | Emergency fund |
| Fixed-term (bond) | Higher rate; money locked for set period | Goal with known date |
| ISA (UK) | Interest earned tax-free | Long-term saving |
| Regular saver | High rate; must deposit monthly | Building a saving habit |
Key Takeaways
- Saving rate = (Amount saved / Income) × 100. Aim for at least 20%.
- Compound interest grows faster than simple interest because interest earns interest.
- Rule of 72: doubling time ≈ 72 / annual rate.
- Starting early matters more than saving large amounts later.
Practice Questions
- Tom saves £200 per month for 5 years. How much has he saved in total (ignoring interest)?
- Find the simple interest on £5 000 at 4% per year for 3 years.
- Find the compound interest earned on £3 000 at 5% per year for 6 years.
- Use the Rule of 72 to estimate how long it takes to double money at 8% per year.
- An emergency fund should cover 4 months of expenses. If monthly essential expenses are £1 350, what is the target emergency fund size?