Subjects finance

Compound Interest Ae3E82

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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.