1. **Stating the problem:** We need to create a simple financial plan for a start-up business involving a loan decision, investment recommendation, and a savings or annuity plan. 2. **Loan comparison:** Suppose two loan options: - Loan A: Simple interest, principal $P=1,000,000$, rate $r=8\%$ per year, time $t=3$ years. - Loan B: Compound interest, principal $P=1,000,000$, rate $r=7\%$ per year compounded annually, time $t=3$ years. Calculate total payments for each. 3. **Loan A (simple interest) calculation:** $$\text{Interest} = P\times r \times t = 1,000,000 \times 0.08 \times 3 = 240,000$$ Total repayment: $$1,000,000 + 240,000 = 1,240,000$$ 4. **Loan B (compound interest) calculation:** $$A = P(1 + r)^t = 1,000,000 (1 + 0.07)^3 = 1,000,000 \times 1.225043 = 1,225,043$$ 5. **Loan choice:** Loan B is cheaper to repay ($1,225,043$) versus Loan A ($1,240,000$). 6. **Investment recommendation:** Invest $500,000 in bonds yielding $5\%$ annually, compounded yearly, for 5 years. Future value: $$FV = 500,000 (1 + 0.05)^5 = 500,000 \times 1.276281 = 638,140.5$$ Expected return is $138,140.5$ after 5 years. 7. **Savings/annuity plan:** Save $10,000$ monthly in an annuity with $4\%$ annual rate compounded monthly for 10 years. Monthly rate: $$r = \frac{0.04}{12} = 0.003333$$ Number of months: $$n = 10 \times 12 = 120$$ Future value of annuity: $$FV = 10,000 \times \frac{(1 + 0.003333)^{120} - 1}{0.003333} = 10,000 \times 148.02 = 1,480,200$$ 8. **Summary:** - Choose Loan B due to lower total cost. - Invest $500,000$ in bonds for steady returns. - Start a monthly annuity savings plan for long-term security with $10,000$/month for 10 years. These choices balance cost, returns, and security for the entrepreneur's start-up.