1. **State the problem:** Bradley takes out a loan of 700 pounds with a compound interest rate of 24% per year. We need to find how much he will owe after 12 years.
2. **Formula for compound interest:**
$$ A = P \left(1 + \frac{r}{100}\right)^t $$
where:
- $A$ is the amount owed after $t$ years,
- $P$ is the principal (initial amount),
- $r$ is the annual interest rate (in percent),
- $t$ is the time in years.
3. **Substitute the values:**
$$ P = 700, \quad r = 24, \quad t = 12 $$
4. **Calculate the amount:**
$$ A = 700 \left(1 + \frac{24}{100}\right)^{12} = 700 \left(1 + 0.24\right)^{12} = 700 \times 1.24^{12} $$
5. **Evaluate $1.24^{12}$:**
$$ 1.24^{12} \approx 14.5519 $$
6. **Multiply by 700:**
$$ A \approx 700 \times 14.5519 = 10186.33 $$
7. **Round to the nearest penny:**
Bradley will owe approximately **10186.33 pounds** after 12 years.
This means the loan grows significantly due to the high compound interest rate over 12 years.
Compound Interest Ae3E82
Step-by-step solutions with LaTeX - clean, fast, and student-friendly.