Finance⏱ 5 min read
How to Calculate Interest on Savings Accounts
Interest rates look simple but the compounding frequency matters — monthly compounding on a 5% account gives you more than annual compounding at 5%. Here's how to calculate precisely.
Banks quote an Annual Interest Rate (AER or AER equivalent), but the compounding frequency underneath that headline rate determines how much you actually earn. Here's the maths behind savings accounts.
Simple Interest vs Compound Interest
Simple interest (rare in savings accounts — mostly short-term bonds):
Interest = Principal x Rate x Time
£5,000 at 5% for 3 years:
Interest = £5,000 x 0.05 x 3 = £750
Total: £5,750
Compound interest (standard for savings accounts):
Amount = Principal x (1 + r)^n
£5,000 at 5% compounded annually for 3 years:
= £5,000 x (1.05)^3 = £5,000 x 1.1576 = £5,788
Difference: £38 more from compounding over 3 years
Compounding Frequency: AER vs Gross Rate
AER (Annual Equivalent Rate) allows fair comparison:
AER = (1 + Gross rate / n)^n - 1
n = number of compounding periods per year
Example: 5% gross rate, monthly compounding
AER = (1 + 0.05/12)^12 - 1 = (1.004167)^12 - 1 = 0.05116 = 5.116%
A 5% gross monthly account is equivalent to 5.116% AER.
Compounding frequency effect on £10,000 over 5 years at 5% gross:
Annual: £10,000 x (1.05)^5 = £12,763
Monthly: £10,000 x (1.004167)^60 = £12,834
Daily: £10,000 x (1+0.05/365)^1825 = £12,840
Continuous: £10,000 x e^(0.05x5) = £12,840
Difference between annual and daily: £77 over 5 years — small but real
Easy Access vs Fixed Rate Accounts
Account TypeFlexibilityRate (typical 2025)
Instant accessWithdraw anytime4.5-5.0% AER
Notice (30/60/90 day)Wait before withdrawal4.8-5.2% AER
1-year fixed bondNo access for 1 year4.6-5.0% AER
2-year fixed bondNo access for 2 years4.4-4.8% AER
Cash ISA (instant)Withdraw anytime, tax-free4.3-4.8% AER
Personal Savings Allowance and Tax
Interest from savings is taxable above your Personal Savings Allowance:
Basic rate taxpayer (20%): £1,000 allowance
Higher rate taxpayer (40%): £500 allowance
Additional rate taxpayer (45%): £0 allowance
Interest earned above allowance is taxed at marginal rate.
At 5% AER, how much savings before you pay tax?
Basic rate: £1,000 / 0.05 = £20,000 in savings
Higher rate: £500 / 0.05 = £10,000 in savings
Above these amounts: use a Cash ISA (tax-free interest)
or a Stocks and Shares ISA for higher potential returns.
Real Return: Adjusting for Inflation
Real return = ((1 + nominal rate) / (1 + inflation rate)) - 1
Savings rate: 5% AER
Inflation: 3.5%
Real return = (1.05 / 1.035) - 1 = 1.0145 - 1 = 1.45%
At 1.45% real return, £10,000 over 10 years:
Real value = £10,000 x (1.0145)^10 = £11,551
(In today's purchasing power — actual nominal balance is higher)