1. **State the problem:** Bradley takes out a loan of 700 pounds with compound interest at 24% per year. We need to find how much he owes 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 %),
- $t$ 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:**
$$A = 700 \times 14.5519 = 10186.33$$
7. **Round to 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 6E2C88
Step-by-step solutions with LaTeX - clean, fast, and student-friendly.