Compound Interest, APR and Loans – Making Financial Maths Real

Ask any GCSE or A-Level Maths student what they’ll use maths for in the real world, and “compound interest” is usually top of the list. Whether it’s savings, loans, or credit cards, understanding how percentages build up over time is an essential life skill.

💷 Simple vs Compound Interest

• Simple interest is just adding the same amount each year.
  £100 at 5% simple interest for 3 years = £115.

• Compound interest is interest on interest.
  £100 at 5% compound interest for 3 years = £115.76.
  It doesn’t look much at first, but over decades the difference is huge.

What is APR and How Does It Work?

APR stands for Annual Percentage Rate – the true yearly cost of borrowing money. Unlike a simple “interest rate,” APR also includes extra charges such as fees, so it gives a fairer picture of what you’ll actually pay.

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💷 A Simple Example

Imagine you borrow £1,000 at 10% simple annual interest:

• After 1 year, you repay £1,100.

• That’s straightforward – interest is £100.

But most loans and credit cards don’t work that simply. They often charge interest monthly or even daily. That’s where APR helps us compare.

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📈 APR with Monthly Interest

Say a credit card charges 1.5% interest per month.
That sounds small – but watch what happens:

• After 1 month: £1,000 → £1,015

• After 12 months: £1,000 grows to about £1,195
  That’s nearly 20% extra in a year, not just 12 × 1.5% = 18%.
  This effect of interest on interest is called compounding.

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⚖ Why APR Matters

APR turns all this into one yearly percentage figure, so you can compare deals fairly.

• A personal loan might have an APR of 6%.

• A credit card might have an APR of 19.9%.

• A payday loan might quote “only 1% per day” – but that works out at over 3,600% APR!

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🎓 Teaching Tip

We use APR in class to show students:

• How a loan can cost far more than its headline rate suggests.

• Why repaying only the “minimum payment” on a credit card keeps debt hanging around for years.

• And why “0% interest” deals are worth double-checking for hidden fees.

APR takes the mystery out of borrowing and turns it into maths students can calculate, compare, and understand.

🏦 Loans and Repayments

Loans use the same maths but in reverse. Borrow £5,000 at 6% over 3 years, and you’ll pay back more than £5,000 – sometimes a lot more depending on the terms. Students are often shocked when they calculate how much that “cheap loan” actually costs over its lifetime.

🎓 Why We Teach It This Way

We use real examples:

• comparing two savings accounts,

• working out the total cost of a loan,

• or even checking how long it takes a credit card debt to vanish if you only pay the minimum.

It turns financial maths from abstract percentages into real decisions they (and their parents!) will one day face. And once students have run the numbers themselves, they’ll never look at an “interest-free” deal the same way again.