1. **Compound Interest Problem:** Given principal $P$, annual interest rate $r$ (as a decimal), number of times interest applied per year $n$, and number of years $t$, the compound interest formula is: $$A = P\left(1 + \frac{r}{n}\right)^{nt}$$ where $A$ is the amount after $t$ years. 2. **Example:** If $P=1000$, $r=0.05$ (5%), $n=1$ (compounded yearly), and $t=3$ years, then: $$A = 1000\left(1 + \frac{0.05}{1}\right)^{1 \times 3} = 1000(1.05)^3$$ Calculate: $$A = 1000 \times 1.157625 = 1157.63$$ So, the amount after 3 years is $1157.63$. 3. **Bearing Problem:** Bearings are measured clockwise from the north direction. If a ship sails on a bearing of $058^\circ$, it means it is $58^\circ$ clockwise from north. 4. **Example:** If a ship travels 10 km on a bearing of $058^\circ$, its eastward (x) and northward (y) components can be found using trigonometry: $$x = 10 \times \sin(58^\circ)$$ $$y = 10 \times \cos(58^\circ)$$ Calculate: $$x \approx 10 \times 0.848 = 8.48 \text{ km}$$ $$y \approx 10 \times 0.529 = 5.29 \text{ km}$$ So, the ship moves approximately 8.48 km east and 5.29 km north. 5. **Summary:** - Use the compound interest formula to calculate amounts over time. - Bearings are angles clockwise from north; use sine and cosine to find components.