Question: Bryn takes out a loan of £800. It gains compound interest at a rate of 28% per year. How much money will Bryn owe after 14 years? Give your answers in pounds to the nearest 1p.
1. **State the problem:**
Bryn borrows £800, and the loan grows with compound interest at a rate of 28% per year. We want to find how much Bryn owes after 14 years.
2. **Formula for compound interest:**
The amount owed after $t$ years with principal $P$ and annual interest rate $r$ compounded yearly is given by:
$$ A = P(1 + r)^t $$
where:
- $A$ is the amount owed after $t$ years,
- $P$ is the initial principal,
- $r$ is the interest rate as a decimal,
- $t$ is the number of years.
3. **Identify values:**
- $P = 800$
- $r = 0.28$ (28% as a decimal)
- $t = 14$
4. **Calculate the amount:**
$$ A = 800(1 + 0.28)^{14} = 800(1.28)^{14} $$
5. **Calculate $(1.28)^{14}$:**
Using a calculator:
$$ (1.28)^{14} \approx 37.699 $$
6. **Multiply by principal:**
$$ A = 800 \times 37.699 = 30159.2 $$
7. **Round to nearest penny:**
The amount Bryn owes after 14 years is approximately:
$$ \boxed{30159.20} $$
So, Bryn will owe £30159.20 after 14 years.