A home was bought with a 20%20% down payment of R177175,00R177175,00. The balance was financed for 2020 years at 9,4%9,4% interest per annum, compounded semi-annually. Find the size of the half-yearly payments for the loan.

To solve this problem, we need to follow these steps:

1. First, we need to find the total price of the home. If R177,175.00 represents the 20% down payment, then the total price is R177,175.00 / 0.20 = R885,875.00.

2. Next, we need to calculate the amount that was financed. This is the total price minus the down payment. So, R885,875.00 - R177,175.00 = R708,700.00.

3. Now, we need to calculate the half-yearly payments. The formula for the payment of a loan is P = [r*PV] / [1 - (1 + r)^-n], where P is the payment, r is the interest rate per period, PV is the present value or principal amount, and n is the number of periods.

4. In this case, the interest rate per period (r) is 9.4% per annum, compounded semi-annually, so r = 9.4% / 2 = 4.7% or 0.047.

5. The number of periods (n) is 20 years, with 2 periods per year, so n = 20 * 2 = 40.

6. Substituting these values into the formula, we get P = [0.047 * R708,700.00] / [1 - (1 + 0.047)^-40].

7. Solving this equation will give us the size of the half-yearly payments for the loan.

To solve this problem, we need to follow these steps:

1. First, we need to find the total price of the home. If R177,175.00 represents the 20% down payment, then the total price is R177,175.00 / 0.20 = R885,875.00.

2. Next, we need to calculate the amount that was financed. This is the total price of the home minus the down payment. So, R885,875.00 - R177,175.00 = R708,700.00.

3. Now, we need to calculate the half-yearly payments. The formula for the payment of a loan is P = [r*PV] / [1 - (1 + r)^-n], where P is the payment, r is the interest rate per period, PV is the present value or loan amount, and n is the number of periods.

4. In this case, the interest rate per period (r) is 9.4% per annum, compounded semi-annually, so r = 9.4% / 2 = 4.7% or 0.047.

5. The number of periods (n) is 20 years, with 2 periods per year, so n = 20 * 2 = 40.

6. Substituting these values into the formula, we get P = [0.047 * R708,700.00] / [1 - (1 + 0.047)^-40].

7. Solving this equation will give us the size of the half-yearly payments for the loan.