1. **State the problem:** Amir and Eva each invest 100000 at 7.5% per annum for 5 years. Amir's interest is compounded daily, Eva's annually. We need to find how much more Amir earned than Eva. 2. **Formulas:** - Compound interest formula: $$A = P \left(1 + \frac{r}{n}\right)^{nt}$$ - Where $A$ is the amount, $P$ is principal, $r$ is annual interest rate (decimal), $n$ is number of compounding periods per year, $t$ is time in years. 3. **Calculate Eva's amount (compounded annually):** - $P = 100000$, $r = 0.075$, $n = 1$, $t = 5$ - $$A_{Eva} = 100000 \left(1 + \frac{0.075}{1}\right)^{1 \times 5} = 100000 (1.075)^5$$ - Calculate $(1.075)^5$: $$1.075^5 = 1.43563$$ - So, $$A_{Eva} = 100000 \times 1.43563 = 143563$$ 4. **Calculate Amir's amount (compounded daily):** - $P = 100000$, $r = 0.075$, $n = 365$, $t = 5$ - $$A_{Amir} = 100000 \left(1 + \frac{0.075}{365}\right)^{365 \times 5} = 100000 \left(1 + 0.00020548\right)^{1825}$$ - Calculate base: $$1 + 0.00020548 = 1.00020548$$ - Calculate exponent: $$1.00020548^{1825} = e^{1825 \times \ln(1.00020548)}$$ - Approximate $\ln(1.00020548) \approx 0.00020546$ - So exponent: $$1825 \times 0.00020546 = 0.3749$$ - Then: $$e^{0.3749} = 1.4543$$ - Therefore: $$A_{Amir} = 100000 \times 1.4543 = 145430$$ 5. **Calculate difference:** - $$\text{Difference} = A_{Amir} - A_{Eva} = 145430 - 143563 = 1867$$ 6. **Final answer:** Amir earned 1867 more than Eva in 5 years.