1. **Stating the problem:** Allan wants to invest 8000 for one year and has two options with different interest rates and compounding frequencies. 2. **Formula for compound interest:** $$A = P \left(1 + \frac{r}{n}\right)^{nt}$$ where: - $A$ is the amount after time $t$ - $P$ is the principal (initial amount) - $r$ is the annual interest rate (decimal) - $n$ is the number of times interest is compounded per year - $t$ is the time in years 3. **Calculate for AAA Bank:** - $P = 8000$ - $r = 0.037$ - $n = 2$ (semi-annually) - $t = 1$ $$A = 8000 \left(1 + \frac{0.037}{2}\right)^{2 \times 1} = 8000 \left(1 + 0.0185\right)^2 = 8000 \times 1.0185^2$$ Calculate $1.0185^2$: $$1.0185^2 = 1.0372225$$ So, $$A = 8000 \times 1.0372225 = 8297.78$$ 4. **Calculate for BBB Bank:** - $P = 8000$ - $r = 0.0375$ - $n = 1$ (annually) - $t = 1$ $$A = 8000 \left(1 + \frac{0.0375}{1}\right)^{1 \times 1} = 8000 \times 1.0375 = 8300$$ 5. **Compare the amounts:** - AAA Bank: 8297.78 - BBB Bank: 8300 6. **Conclusion:** Allan should choose BBB Bank because it yields a slightly higher amount after one year, despite AAA Bank compounding semi-annually. The difference is small but BBB Bank offers better returns.