Calculate the total expenses and determine if they are within the aunt's budget of shs. 5,000,000, given the scholarship details.

The original school fees are shs. 3,000,000. The scholarship offers a 50% discount on school fees.

$$\text{Discount amount} = 0.50 \times \text{shs. } 3,000,000 = \text{shs. } 1,500,000$$ $$\text{New school fees} = \text{shs. } 3,000,000 - \text{shs. } 1,500,000 = \text{shs. } 1,500,000$$

The original boarding fees are shs. 1,500,000. The scholarship offers a shs. 200,000 reduction.

$$\text{New boarding fees} = \text{shs. } 1,500,000 - \text{shs. } 200,000 = \text{shs. } 1,300,000$$

The original cost of school supplies is shs. 500,000. The scholarship offers a shs. 150,000 voucher.

$$\text{New school supplies cost} = \text{shs. } 500,000 - \text{shs. } 150,000 = \text{shs. } 350,000$$

The total expenses are the sum of the new school fees, new boarding fees, and new school supplies cost.

$$\text{Total expenses} = \text{shs. } 1,500,000 + \text{shs. } 1,300,000 + \text{shs. } 350,000 = \text{shs. } 3,150,000$$

The aunt's budget is shs. 5,000,000, so the total expenses are within the budget.

The new school fees are shs. 1,500,000. Option 1 involves two installments: two-fifths at the beginning of the term and the balance before midterm exams.

$$\text{First installment} = \frac{2}{5} \times \text{shs. } 1,500,000 = 2 \times \text{shs. } 300,000 = \text{shs. } 600,000$$ $$\text{Second installment} = \text{shs. } 1,500,000 - \text{shs. } 600,000 = \text{shs. } 900,000$$

Under Option 1, the payments would be shs. 600,000 at the beginning of the term and shs. 900,000 before midterm exams.

The new school fees are shs. 1,500,000. Option 2 involves four equal installments.

$$\text{Amount per installment} = \frac{\text{shs. } 1,500,000}{4} = \text{shs. } 375,000$$

Under Option 2, four equal payments of shs. 375,000 would be made at the beginning of the term, before midterm exams, after midterm, and before final exams.

The total expenses after the scholarship are $\text{shs. } 3,150,000$.