Mr. Fourie buys ‘n farm with a cash price of R 990 000. He pays a deposit of R 180 000 and arranges a loan through Land Bank South-Africa for the remainder of the cash price. This loan has to be repaid in equal semi-annual instalments at the end of each 6-month period over 18 years and interest will be compounded semi-annually at a rate of 16% per annum. What will the value of the semi-annual instalments be?

Answer 1

First, let's calculate the loan amount that Mr. Fourie will need from Land Bank South-Africa:

Loan amount = Cash price - Deposit
Loan amount = R 990,000 - R 180,000
Loan amount = R 810,000

Next, we need to calculate the semi-annual interest rate:
Semi-annual interest rate = Annual interest rate / 2
Semi-annual interest rate = 16% / 2
Semi-annual interest rate = 8%

Now, we can calculate the value of the semi-annual instalments using the formula for the loan repayment amount:

Loan repayment amount = Loan amount * (r(1 + r)^n) / ((1 + r)^n - 1)

Where:
- Loan amount = R 810,000
- r = semi-annual interest rate = 8% or 0.08
- n = number of periods = 18 years * 2 semi-annual periods per year = 36

Plugging in the values:

Loan repayment amount = R 810,000 * (0.08(1 + 0.08)^36) / ((1 + 0.08)^36 - 1)
Loan repayment amount = R 810,000 * (0.08(2.08)^36) / (2.08^36 - 1)
Loan repayment amount = R 810,000 * (0.08 * 187.576) / (187.576 - 1)
Loan repayment amount = R 810,000 * 15.006 / 186.576
Loan repayment amount = R 12133.44

Therefore, the value of the semi-annual instalments will be approximately R 12,133.44.