Compound Interest – How Money Grows (or Doesn’t)

Compound interest is one of the most practical applications of maths. It explains how savings can grow steadily over time — and how debts can spiral if repayments are delayed.

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Simple vs Compound Interest

• Simple interest adds the same amount each year.
  Example: £100 at 5% simple interest for 3 years grows to £115.

• Compound interest adds interest on the new total each year.
  Example: £100 at 5% compound interest for 3 years grows to about £115.76.

The difference looks small at first, but over decades it becomes enormous.

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The Formula

$$A = P \left(1 + \frac{r}{100}\right)^n$$

Where:

• $A$ = total amount

• $P$ = starting amount (the principal)

• $r$ = interest rate (%)

• $n$ = number of years

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A Worked Example

Suppose you invest £1,000 at 5% compound interest for 10 years.

$$A = 1000 \times (1.05)^{10} = £1628.89$$

That is £628.89 earned just by leaving the money in the account.

But debt works the same way. Borrow £1,000 on a credit card at 20% interest without paying it back for 10 years:

$$A = 1000 \times (1.20)^{10} = £6191.74$$

That’s six times the original amount.

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Why It Matters

Understanding compound interest helps students see:

• Why saving early makes a big difference.

• Why paying off debt quickly is essential.

• How percentages apply directly to everyday life.

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What is APR?

APR stands for Annual Percentage Rate. It’s the true yearly cost of borrowing money.

When you borrow using a loan, credit card, or finance deal, you don’t just pay back what you borrowed — you also pay extra in interest and sometimes fees. APR combines all of this into one percentage figure so you can compare deals fairly.

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How does it work?

• If a bank offers you £1,000 at 10% APR, you’ll pay about £100 extra over the year.

• If another bank offers the same £1,000 at 20% APR, you’ll pay about £200 extra over the year.

That’s why looking at the APR lets you see which loan really costs less.

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Why not just look at the monthly rate?

Because interest is usually compounded (added on to what you already owe).
For example:

• A credit card might charge 1.5% each month.

• Over 12 months that’s not just 18% (12 × 1.5%), but closer to 20% once compounding is included.

• The APR takes this into account.

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Why is it useful?

APR is like the “price tag” of borrowing.
It helps you answer:

• Which loan is cheapest?

• How much will this credit really cost me?

• Should I borrow at all?

Conclusion

Compound interest shows how money doesn’t just sit still — it grows, for better or worse. Learning the maths behind it gives students real-world financial awareness and a powerful life skill.