An individual needs to pay three installments to pay off the purchase of land. Compound interest of 30% per semester is charged. The installments are R$120,000.00, R$180,000.00 and R$338,000.00 and mature in six months, one year and two years, respectively. These three payments can be replaced by a single payment, one year from now, in the amount, in reais, of:

To calculate the equivalent single payment one year from now that would replace the three installment payments with compound interest of 30% per semester, we first need to adjust each future payment to its present value (PV) at one year from now, and then sum these values. This is because the question asks for the single payment amount at the one-year point, not at the present time.

Given the future installment payments and their due times:
1. R\$120,000.00 due in 6 months.
2. R\$180,000.00 due in 1 year.
3. R\$338,000.00 due in 2 years.

The formula for calculating the present value of a future payment is:PV = \dfrac{F}{(1 + r)^n} where F is the future payment, r is the interest rate per period, and n is the number of periods until the payment is made.

### Step 1: Convert all future payments to their present values at one year from now
- For R\$120,000.00 due in 6 months: PV_{6 \text{ months}} = \dfrac{120,000}{1.3}
- For R\$180,000.00 due in 1 year: PV_{1 \text{ year}} = 180,000
- For R\$338,000.00 due in 2 years: PV_{2 \text{ years}} = \dfrac{338,000}{1.3^2}

### Step 2: Use the formula
Calculating the present values:
- PV_{6 \text{ months}} = \dfrac{120,000}{1.3} \approx R\$92,307.69
- PV_{1 \text{ year}} = 180,000
- PV_{2 \text{ years}} = \dfrac{338,000}{1.3^2} \approx R\$200,000.00

### Answer
The total equivalent single payment one year from now is approximately R\$472,307.69.