1. **Stating the Problem:** You need to create a financial plan for a start-up business, including loan comparison, investment recommendations, and savings or annuity planning. 2. **Loan Comparison:** Assume two loans: Loan A with simple interest and Loan B with compound interest. - Simple Interest formula: $$I = P \times r \times t$$ - Compound Interest formula: $$A = P \times \left(1 + \frac{r}{n}\right)^{nt}$$ Let’s say the capital needed is 500,000, annual interest rate 5%, period 3 years. 3. **Calculate Simple Interest (Loan A):** $$I = 500000 \times 0.05 \times 3 = 75000$$ Total to repay: $$500000 + 75000 = 575000$$ 4. **Calculate Compound Interest (Loan B, compounded annually):** $$A = 500000 \times (1 + 0.05)^3 = 500000 \times 1.157625 = 578812.5$$ 5. **Loan Choice:** Loan A repayment is 575000; Loan B repayment is 578812.5. Loan A is slightly cheaper and simpler. 6. **Investment Recommendation:** Invest 300,000 of capital in stocks or bonds: - Expected annual return for stocks: 8% - Expected annual return for bonds: 5% Compute annual expected return for stocks: $$300000 \times 0.08 = 24000$$ For bonds: $$300000 \times 0.05 = 15000$$ Recommend stocks for higher return despite higher risk. 7. **Savings/Annuity Plan:** Plan to save 50,000 yearly at 4% interest over 5 years. Use formula for future value of an ordinary annuity: $$FV = P \times \frac{(1 + r)^t - 1}{r}$$ Calculate: $$FV = 50000 \times \frac{(1 + 0.04)^5 - 1}{0.04} = 50000 \times 5.4163 = 270815$$ 8. **Summary:** - Choose Loan A (simple interest, less total repayment). - Invest 300,000 in stocks for higher expected returns. - Set up annuity savings plan saving 50,000 yearly for 5 years to grow to about 270,815. This plan balances cost of loan, investment returns, and savings growth effectively.