Subjects finance

Compound Interest 83948E

Step-by-step solutions with LaTeX - clean, fast, and student-friendly.

Use the AI math solver

1. **Problem statement:** Oscar invests 2000 pounds into a savings account with a compound interest rate of 3.5% per year. We need to find: a) The total amount in the account after 9 years. b) The total interest earned after 9 years. 2. **Formula for compound interest:** $$A = P \left(1 + \frac{r}{100}\right)^t$$ where: - $A$ is the amount after $t$ years, - $P$ is the principal (initial amount), - $r$ is the annual interest rate (in %), - $t$ is the time in years. 3. **Calculate the amount after 9 years:** Given $P = 2000$, $r = 3.5$, and $t = 9$, $$A = 2000 \left(1 + \frac{3.5}{100}\right)^9 = 2000 \left(1 + 0.035\right)^9 = 2000 \times 1.035^9$$ Calculate $1.035^9$: $$1.035^9 \approx 1.372786$$ So, $$A \approx 2000 \times 1.372786 = 2745.572$$ Rounded to the nearest penny: $$A = 2745.57$$ 4. **Calculate the interest earned:** Interest $I = A - P$ $$I = 2745.57 - 2000 = 745.57$$ 5. **Final answers:** a) Oscar will have **2745.57** pounds in the account after 9 years. b) The interest earned after 9 years is **745.57** pounds.