Why do you multiply by 1.07 if you’re adding 7%? I thought 7% was 0.07.

You’re quite right - 0.07 is exactly the same thing as 7% (and, if you like, $\frac{7}{100}$). However, if you’re adding on 7%, you need to multiply by 1.07, and here’s why.

Let’s say you’re adding 7% to 1000: you’d be working out $1000 + 1000 \times 0.07$ - or, better still, $1000\left( 1 + 0.07 \right)$. That thing in the bracket is 1.07.

The short reason: because you’re adding 7% on to what’s already there, you need to multiply it by 1 + the percentage as a decimal.