How to Calculate Interest — Simple vs Compound (APR ↔ APY)

The Two Types of Interest: Simple vs. Compound

1. Simple Interest: Linear Growth

Simple interest is calculated only on the original principal amount for the entire duration of the loan or investment. It’s straightforward and rarely used for long-term savings, but common in short-term loans and bonds.

Formula:
I = P × r × t
A = P + I = P(1 + r × t)

Where:

• I = Total interest
• A = Final amount (principal + interest)
• P = Principal (initial amount)
• r = Annual interest rate (decimal)
• t = Time in years

Example:
£2,000 at 5% simple interest for 3 years:
I = 2000 × 0.05 × 3 = £300
A = £2,300

2. Compound Interest: Exponential Growth

Compound interest is calculated on the principal plus all previously accumulated interest. This creates a snowball effect where your money grows faster over time—earning “interest on interest.” This is the standard for savings accounts, investments, and most loans.

Formula:
A = P × (1 + r/n)^(n×t)

Where:

• n = Number of compounding periods per year (e.g., 12 for monthly)

Example:
£2,000 at 5% compounded monthly for 3 years:
A = 2000 × (1 + 0.05/12)^(12×3) ≈ £2,323.82
£23.82 more than simple interest—just from compounding.

3. Continuous Compounding: The Theoretical Maximum

In theory, interest can be compounded infinitely often. This uses Euler’s number (e ≈ 2.71828):

Formula:
A = P × e^(r×t)

Example:
Same £2,000 at 5% for 3 years:
A = 2000 × e^(0.05×3) ≈ £2,323.92
Only £0.10 more than monthly compounding—showing diminishing returns.

APR vs. APY: The Critical Distinction

• APR (Annual Percentage Rate): The nominal annual rate without compounding. Used for loans and credit cards.
• APY (Annual Percentage Yield): The effective annual rate with compounding. Used for savings and investments.

APY Formula:
APY = (1 + r/n)^n – 1

Example:
A 5% APR compounded monthly:
APY = (1 + 0.05/12)^12 – 1 ≈ 5.116%

This means a 5% APR savings account actually yields 5.116% annually. Always compare APYs—not APRs—when choosing savings products.

Step-by-Step Interest Calculations

For Savings/Investments:

1. Identify P, r, n, and t.
2. Apply the compound interest formula.
3. Subtract P to find total interest earned.

For Loans:

1. Use the same formula to find total repayment (A).
2. Total interest = A – P.
3. For credit cards, interest compounds daily—use n = 365.

For Debt Cost Analysis:

• A £5,000 credit card balance at 24% APR (compounded daily) grows to £6,341 in one year if unpaid.
• The same amount in a 2% APY savings account grows to only £5,101.

Pro Tips & Best Practices

• Maximise compounding: Choose accounts with daily or monthly compounding over annual.
• Start early: Time magnifies compounding. £100/month at 7% from age 25 → £245,000 by 65. From age 35 → £125,000.
• Minimise debt interest: Pay off high-APR debt first. A 24% credit card costs far more than a 3% mortgage earns.
• Reinvest earnings: Enable dividend reinvestment in stocks to harness compounding.
• Beware of fees: A 1% annual fee can erase 15–20% of your returns over 30 years.

Practical Applications

• Savings goals: Calculate monthly deposits needed to reach a target (use our Investment Calculator).
• Loan comparisons: A 4% APR car loan vs. 5%—the difference is £500+ over 5 years on a £20,000 loan.
• Credit card strategy: Paying only the minimum on a £3,000 balance at 22% APR takes 15+ years and costs £4,000+ in interest.
• Retirement planning: Compound growth is the engine of long-term wealth—start early and stay consistent.