Compound Interest 5B1Dfa

1. **State the problem:** A businesswoman invests 350000 at an interest rate of 6% compounded yearly. We need to find the total amount after 8 years. 2. **Formula used:** The formula for compound interest is: $$ A = P \left(1 + \frac{r}{n}\right)^{nt} $$ where: - $A$ is the amount after time $t$ - $P$ is the principal amount (350000) - $r$ is the annual interest rate (0.06) - $n$ is the number of times interest is compounded per year (1 for yearly) - $t$ is the number of years (8) 3. **Substitute the values:** $$ A = 350000 \left(1 + \frac{0.06}{1}\right)^{1 \times 8} = 350000 \left(1.06\right)^8 $$ 4. **Calculate the power:** $$ 1.06^8 = 1.593848 $$ 5. **Calculate the amount:** $$ A = 350000 \times 1.593848 = 557846.8 $$ 6. **Interpretation:** The total amount of money she would have at the end of 8 years is approximately 557847. 7. **Explanation of technique:** The technique used is compound interest calculation, where interest is added to the principal yearly, and the next year's interest is calculated on the new principal including previous interest. This causes the amount to grow exponentially rather than linearly.